LMFDB - Embedded newform 19.9.f.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,9,Mod(2,19)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.74019359116$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	19.2
Dual form			19.9.f.a.10.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.0012 - 1.76348i) q^{2} +(-70.0946 + 83.5355i) q^{3} +(-143.647 - 52.2832i) q^{4} +(-433.854 + 157.910i) q^{5} +(848.344 - 711.845i) q^{6} +(171.924 + 297.780i) q^{7} +(3595.94 + 2076.12i) q^{8} +(-925.619 - 5249.44i) q^{9} +O(q^{10})$	\(q+(-10.0012 - 1.76348i) q^{2} +(-70.0946 + 83.5355i) q^{3} +(-143.647 - 52.2832i) q^{4} +(-433.854 + 157.910i) q^{5} +(848.344 - 711.845i) q^{6} +(171.924 + 297.780i) q^{7} +(3595.94 + 2076.12i) q^{8} +(-925.619 - 5249.44i) q^{9} +(4617.53 - 814.196i) q^{10} +(7011.43 - 12144.1i) q^{11} +(14436.4 - 8334.85i) q^{12} +(-13218.7 - 15753.4i) q^{13} +(-1194.31 - 3281.35i) q^{14} +(17219.7 - 47310.8i) q^{15} +(-2324.45 - 1950.45i) q^{16} +(-1335.04 + 7571.41i) q^{17} +54133.1i q^{18} +(101701. + 81488.8i) q^{19} +70577.8 q^{20} +(-36926.1 - 6511.08i) q^{21} +(-91538.8 + 109092. i) q^{22} +(-229033. - 83361.3i) q^{23} +(-425486. + 154864. i) q^{24} +(-135943. + 114069. i) q^{25} +(104422. + 180864. i) q^{26} +(-116213. - 67095.7i) q^{27} +(-9127.39 - 51764.0i) q^{28} +(535510. - 94424.9i) q^{29} +(-255650. + 442799. i) q^{30} +(1.05427e6 - 608684. i) q^{31} +(-663458. - 790678. i) q^{32} +(523004. + 1.43694e6i) q^{33} +(26704.1 - 73368.9i) q^{34} +(-121612. - 102045. i) q^{35} +(-141496. + 802461. i) q^{36} -1.83694e6i q^{37} +(-873432. - 994335. i) q^{38} +2.24253e6 q^{39} +(-1.88795e6 - 332897. i) q^{40} +(1.59596e6 - 1.90199e6i) q^{41} +(357824. + 130237. i) q^{42} +(-292512. + 106466. i) q^{43} +(-1.64211e6 + 1.37789e6i) q^{44} +(1.23052e6 + 2.13133e6i) q^{45} +(2.14360e6 + 1.23761e6i) q^{46} +(-757660. - 4.29690e6i) q^{47} +(325863. - 57458.4i) q^{48} +(2.82329e6 - 4.89007e6i) q^{49} +(1.56075e6 - 901099. i) q^{50} +(-538902. - 642238. i) q^{51} +(1.07519e6 + 2.95405e6i) q^{52} +(-2.47545e6 + 6.80124e6i) q^{53} +(1.04395e6 + 875979. i) q^{54} +(-1.12425e6 + 6.37596e6i) q^{55} +1.42774e6i q^{56} +(-1.39359e7 + 2.78374e6i) q^{57} -5.52227e6 q^{58} +(-2.07133e7 - 3.65232e6i) q^{59} +(-4.94712e6 + 5.89575e6i) q^{60} +(1.79348e7 + 6.52773e6i) q^{61} +(-1.16174e7 + 4.22839e6i) q^{62} +(1.40405e6 - 1.17813e6i) q^{63} +(5.62943e6 + 9.75046e6i) q^{64} +(8.22260e6 + 4.74732e6i) q^{65} +(-2.69665e6 - 1.52935e7i) q^{66} +(2.76178e7 - 4.86976e6i) q^{67} +(587632. - 1.01781e6i) q^{68} +(2.30176e7 - 1.32892e7i) q^{69} +(1.03631e6 + 1.23503e6i) q^{70} +(-1.51678e7 - 4.16733e7i) q^{71} +(7.57000e6 - 2.07984e7i) q^{72} +(2.52093e7 + 2.11531e7i) q^{73} +(-3.23941e6 + 1.83716e7i) q^{74} -1.93517e7i q^{75} +(-1.03486e7 - 1.70229e7i) q^{76} +4.82172e6 q^{77} +(-2.24280e7 - 3.95466e6i) q^{78} +(-3.01155e7 + 3.58902e7i) q^{79} +(1.31647e6 + 479155. i) q^{80} +(4.66146e7 - 1.69663e7i) q^{81} +(-1.93156e7 + 1.62078e7i) q^{82} +(-1.42612e7 - 2.47012e7i) q^{83} +(4.96391e6 + 2.86591e6i) q^{84} +(-616386. - 3.49570e6i) q^{85} +(3.11323e6 - 548946. i) q^{86} +(-2.96485e7 + 5.13528e7i) q^{87} +(5.04254e7 - 2.91131e7i) q^{88} +(-1.33770e6 - 1.59421e6i) q^{89} +(-8.54815e6 - 2.34859e7i) q^{90} +(2.41846e6 - 6.64466e6i) q^{91} +(2.85415e7 + 2.39492e7i) q^{92} +(-2.30520e7 + 1.30734e8i) q^{93} +4.43104e7i q^{94} +(-5.69913e7 - 1.92946e7i) q^{95} +1.12554e8 q^{96} +(-1.10420e8 - 1.94699e7i) q^{97} +(-3.68598e7 + 4.39278e7i) q^{98} +(-7.02399e7 - 2.55652e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9}+O(q^{10}) $ 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9} - 2793 q^{10} + 10482 q^{11} - 124425 q^{12} + 108465 q^{13} + 91905 q^{14} - 236277 q^{15} - 207120 q^{16} + 40269 q^{17} + 188304 q^{19} + 1700646 q^{20} + 386850 q^{21} - 1237254 q^{22} - 1339566 q^{23} - 1289928 q^{24} + 59748 q^{25} - 842907 q^{26} + 4849875 q^{27} - 2065044 q^{28} - 1312269 q^{29} + 299940 q^{30} + 3498759 q^{31} + 9109881 q^{32} - 1670298 q^{33} - 12448236 q^{34} - 5923416 q^{35} - 6763797 q^{36} + 5067372 q^{38} + 18303516 q^{39} + 15014562 q^{40} - 11716206 q^{41} - 9228981 q^{42} + 12974721 q^{43} - 2631387 q^{44} - 31264995 q^{45} - 30318354 q^{46} + 1571889 q^{47} + 55683057 q^{48} + 1898838 q^{49} + 30782124 q^{50} + 12474372 q^{51} - 839439 q^{52} - 49160157 q^{53} - 65504571 q^{54} - 27903114 q^{55} + 18105312 q^{57} + 85061964 q^{58} + 51376881 q^{59} + 61200294 q^{60} - 51972462 q^{61} - 85396644 q^{62} + 41912118 q^{63} - 35891445 q^{64} + 2267586 q^{65} + 53209500 q^{66} + 35494521 q^{67} + 13755102 q^{68} + 54287784 q^{69} + 98126001 q^{70} - 5729388 q^{71} - 580668798 q^{72} - 255453906 q^{73} + 159588693 q^{74} + 128877954 q^{76} + 345629838 q^{77} + 120889431 q^{78} + 73477881 q^{79} - 93973551 q^{80} + 114909627 q^{81} + 67089591 q^{82} + 55994352 q^{83} + 143496459 q^{84} - 29709876 q^{85} - 592637892 q^{86} - 151341879 q^{87} - 412023537 q^{88} - 7283562 q^{89} + 350808846 q^{90} + 81065763 q^{91} + 496900692 q^{92} - 609570561 q^{93} - 222935505 q^{95} + 89754174 q^{96} - 180436449 q^{97} + 472058181 q^{98} + 865983036 q^{99}+O(q^{100}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9 - 2793 * q^10 + 10482 * q^11 - 124425 * q^12 + 108465 * q^13 + 91905 * q^14 - 236277 * q^15 - 207120 * q^16 + 40269 * q^17 + 188304 * q^19 + 1700646 * q^20 + 386850 * q^21 - 1237254 * q^22 - 1339566 * q^23 - 1289928 * q^24 + 59748 * q^25 - 842907 * q^26 + 4849875 * q^27 - 2065044 * q^28 - 1312269 * q^29 + 299940 * q^30 + 3498759 * q^31 + 9109881 * q^32 - 1670298 * q^33 - 12448236 * q^34 - 5923416 * q^35 - 6763797 * q^36 + 5067372 * q^38 + 18303516 * q^39 + 15014562 * q^40 - 11716206 * q^41 - 9228981 * q^42 + 12974721 * q^43 - 2631387 * q^44 - 31264995 * q^45 - 30318354 * q^46 + 1571889 * q^47 + 55683057 * q^48 + 1898838 * q^49 + 30782124 * q^50 + 12474372 * q^51 - 839439 * q^52 - 49160157 * q^53 - 65504571 * q^54 - 27903114 * q^55 + 18105312 * q^57 + 85061964 * q^58 + 51376881 * q^59 + 61200294 * q^60 - 51972462 * q^61 - 85396644 * q^62 + 41912118 * q^63 - 35891445 * q^64 + 2267586 * q^65 + 53209500 * q^66 + 35494521 * q^67 + 13755102 * q^68 + 54287784 * q^69 + 98126001 * q^70 - 5729388 * q^71 - 580668798 * q^72 - 255453906 * q^73 + 159588693 * q^74 + 128877954 * q^76 + 345629838 * q^77 + 120889431 * q^78 + 73477881 * q^79 - 93973551 * q^80 + 114909627 * q^81 + 67089591 * q^82 + 55994352 * q^83 + 143496459 * q^84 - 29709876 * q^85 - 592637892 * q^86 - 151341879 * q^87 - 412023537 * q^88 - 7283562 * q^89 + 350808846 * q^90 + 81065763 * q^91 + 496900692 * q^92 - 609570561 * q^93 - 222935505 * q^95 + 89754174 * q^96 - 180436449 * q^97 + 472058181 * q^98 + 865983036 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−10.0012	−	1.76348i	−0.625076	−	0.110218i	−0.147866	−	0.989007i	$-0.547241\pi$
$2$	−10.0012	−	1.76348i	−0.625076	−	0.110218i	−0.477209	+	0.878790i	$0.658352\pi$
$3$	−70.0946	+	83.5355i	−0.865365	+	1.03130i	0.133823	+	0.991005i	$0.457275\pi$
$3$	−70.0946	+	83.5355i	−0.865365	+	1.03130i	−0.999188	+	0.0402968i	$0.987170\pi$
$4$	−143.647	−	52.2832i	−0.561121	−	0.204231i
$5$	−433.854	+	157.910i	−0.694166	+	0.252656i	−0.664918	−	0.746916i	$-0.731533\pi$
$5$	−433.854	+	157.910i	−0.694166	+	0.252656i	−0.0292480	+	0.999572i	$0.509311\pi$
$6$	848.344	−	711.845i	0.654587	−	0.549263i
$7$	171.924	+	297.780i	0.0716050	+	0.124024i	0.899605	−	0.436705i	$-0.143855\pi$
$7$	171.924	+	297.780i	0.0716050	+	0.124024i	−0.828000	+	0.560728i	$0.810521\pi$
$8$	3595.94	+	2076.12i	0.877916	+	0.506865i
$9$	−925.619	−	5249.44i	−0.141079	−	0.800098i
$10$	4617.53	−	814.196i	0.461753	−	0.0814196i
$11$	7011.43	−	12144.1i	0.478890	−	0.829462i	−0.520817	−	0.853668i	$-0.674373\pi$
$11$	7011.43	−	12144.1i	0.478890	−	0.829462i	0.999707	+	0.0242067i	$0.00770598\pi$
$12$	14436.4	−	8334.85i	0.696199	−	0.401950i
$13$	−13218.7	−	15753.4i	−0.462823	−	0.551571i	0.483268	−	0.875473i	$-0.339450\pi$
$13$	−13218.7	−	15753.4i	−0.462823	−	0.551571i	−0.946091	+	0.323901i	$0.895005\pi$
$14$	−1194.31	−	3281.35i	−0.0310890	−	0.0854162i
$15$	17219.7	−	47310.8i	0.340143	−	0.934534i
$16$	−2324.45	−	1950.45i	−0.0354683	−	0.0297615i
$17$	−1335.04	+	7571.41i	−0.0159845	+	0.0906527i	−0.991756	−	0.128138i	$-0.959100\pi$
$17$	−1335.04	+	7571.41i	−0.0159845	+	0.0906527i	0.975772	+	0.218791i	$0.0702111\pi$
$18$			54133.1i			0.515671i
$19$	101701.	+	81488.8i	0.780390	+	0.625293i
$19$	101701.	+	81488.8i	0.780390	+	0.625293i
$20$	70577.8			0.441111
$21$	−36926.1	−	6511.08i	−0.189870	−	0.0334792i
$22$	−91538.8	+	109092.i	−0.390764	+	0.465694i
$23$	−229033.	−	83361.3i	−0.818441	−	0.297888i	−0.101335	−	0.994852i	$-0.532311\pi$
$23$	−229033.	−	83361.3i	−0.818441	−	0.297888i	−0.717106	+	0.696964i	$0.754534\pi$
$24$	−425486.	+	154864.i	−1.28245	+	0.466773i
$25$	−135943.	+	114069.i	−0.348013	+	0.292018i
$26$	104422.	+	180864.i	0.228507	+	0.395785i
$27$	−116213.	−	67095.7i	−0.218676	−	0.126252i
$28$	−9127.39	−	51764.0i	−0.0148496	−	0.0842162i
$29$	535510.	−	94424.9i	0.757139	−	0.133504i	0.218264	−	0.975890i	$-0.429961\pi$
$29$	535510.	−	94424.9i	0.757139	−	0.133504i	0.538875	+	0.842386i	$0.318850\pi$
$30$	−255650.	+	442799.i	−0.315617	+	0.546665i
$31$	1.05427e6	−	608684.i	1.14158	−	0.659090i	0.194757	−	0.980851i	$-0.437608\pi$
$31$	1.05427e6	−	608684.i	1.14158	−	0.659090i	0.946821	+	0.321761i	$0.104275\pi$
$32$	−663458.	−	790678.i	−0.632723	−	0.754049i
$33$	523004.	+	1.43694e6i	0.441011	+	1.21167i
$34$	26704.1	−	73368.9i	0.0199831	−	0.0549031i
$35$	−121612.	−	102045.i	−0.0810410	−	0.0680015i
$36$	−141496.	+	802461.i	−0.0842428	+	0.477765i
$37$		−	1.83694e6i		−	0.980140i	−0.871683	−	0.490070i	$-0.836971\pi$
$37$		−	1.83694e6i		−	0.980140i	0.871683	−	0.490070i	$-0.163029\pi$
$38$	−873432.	−	994335.i	−0.418885	−	0.476868i
$39$	2.24253e6			0.969348
$40$	−1.88795e6	−	332897.i	−0.737481	−	0.130038i
$41$	1.59596e6	−	1.90199e6i	0.564789	−	0.673089i	−0.405764	−	0.913978i	$-0.632994\pi$
$41$	1.59596e6	−	1.90199e6i	0.564789	−	0.673089i	0.970553	+	0.240889i	$0.0774389\pi$
$42$	357824.	+	130237.i	0.114993	+	0.0418541i
$43$	−292512.	+	106466.i	−0.0855600	+	0.0311413i	−0.384446	−	0.923148i	$-0.625607\pi$
$43$	−292512.	+	106466.i	−0.0855600	+	0.0311413i	0.298886	+	0.954289i	$0.403385\pi$
$44$	−1.64211e6	+	1.37789e6i	−0.438117	+	0.367624i
$45$	1.23052e6	+	2.13133e6i	0.300082	+	0.519757i
$46$	2.14360e6	+	1.23761e6i	0.478755	+	0.276409i
$47$	−757660.	−	4.29690e6i	−0.155268	−	0.880571i	−0.958540	−	0.284958i	$-0.908020\pi$
$47$	−757660.	−	4.29690e6i	−0.155268	−	0.880571i	0.803272	−	0.595613i	$-0.203091\pi$
$48$	325863.	−	57458.4i	0.0613861	−	0.0108240i
$49$	2.82329e6	−	4.89007e6i	0.489745	−	0.848264i
$50$	1.56075e6	−	901099.i	0.249720	−	0.144176i
$51$	−538902.	−	642238.i	−0.0796579	−	0.0949326i
$52$	1.07519e6	+	2.95405e6i	0.147052	+	0.404021i
$53$	−2.47545e6	+	6.80124e6i	−0.313726	+	0.861955i	0.678170	+	0.734905i	$0.262773\pi$
$53$	−2.47545e6	+	6.80124e6i	−0.313726	+	0.861955i	−0.991896	+	0.127050i	$0.959449\pi$
$54$	1.04395e6	+	875979.i	0.122774	+	0.103019i
$55$	−1.12425e6	+	6.37596e6i	−0.122861	+	0.696778i
$56$			1.42774e6i			0.145176i
$57$	−1.39359e7	+	2.78374e6i	−1.32019	+	0.263711i
$58$	−5.52227e6			−0.487984
$59$	−2.07133e7	−	3.65232e6i	−1.70939	−	0.301412i	−0.768433	−	0.639931i	$-0.778963\pi$
$59$	−2.07133e7	−	3.65232e6i	−1.70939	−	0.301412i	−0.940960	+	0.338519i	$0.890074\pi$
$60$	−4.94712e6	+	5.89575e6i	−0.381722	+	0.454919i
$61$	1.79348e7	+	6.52773e6i	1.29532	+	0.471458i	0.895469	−	0.445123i	$-0.146840\pi$
$61$	1.79348e7	+	6.52773e6i	1.29532	+	0.471458i	0.399850	+	0.916581i	$0.369062\pi$
$62$	−1.16174e7	+	4.22839e6i	−0.786216	+	0.286159i
$63$	1.40405e6	−	1.17813e6i	0.0891290	−	0.0747881i
$64$	5.62943e6	+	9.75046e6i	0.335540	+	0.581173i
$65$	8.22260e6	+	4.74732e6i	0.460634	+	0.265947i
$66$	−2.69665e6	−	1.52935e7i	−0.142118	−	0.805991i
$67$	2.76178e7	−	4.86976e6i	1.37053	−	0.241662i	0.560552	−	0.828119i	$-0.310589\pi$
$67$	2.76178e7	−	4.86976e6i	1.37053	−	0.241662i	0.809980	+	0.586457i	$0.199478\pi$
$68$	587632.	−	1.01781e6i	0.0274834	−	0.0476026i
$69$	2.30176e7	−	1.32892e7i	1.01546	−	0.586278i
$70$	1.03631e6	+	1.23503e6i	0.0431618	+	0.0514382i
$71$	−1.51678e7	−	4.16733e7i	−0.596885	−	1.63993i	−0.757443	−	0.652901i	$-0.773552\pi$
$71$	−1.51678e7	−	4.16733e7i	−0.596885	−	1.63993i	0.160559	−	0.987026i	$-0.448670\pi$
$72$	7.57000e6	−	2.07984e7i	0.281686	−	0.773927i
$73$	2.52093e7	+	2.11531e7i	0.887705	+	0.744873i	0.967749	−	0.251918i	$-0.0810614\pi$
$73$	2.52093e7	+	2.11531e7i	0.887705	+	0.744873i	−0.0800431	+	0.996791i	$0.525506\pi$
$74$	−3.23941e6	+	1.83716e7i	−0.108029	+	0.612662i
$75$		−	1.93517e7i		−	0.611608i
$76$	−1.03486e7	−	1.70229e7i	−0.310189	−	0.510245i
$77$	4.82172e6			0.137164
$78$	−2.24280e7	−	3.95466e6i	−0.605916	−	0.106839i
$79$	−3.01155e7	+	3.58902e7i	−0.773181	+	0.921441i	−0.998604	−	0.0528196i	$-0.983179\pi$
$79$	−3.01155e7	+	3.58902e7i	−0.773181	+	0.921441i	0.225423	+	0.974261i	$0.427624\pi$
$80$	1.31647e6	+	479155.i	0.0321403	+	0.0116981i
$81$	4.66146e7	−	1.69663e7i	1.08288	−	0.394137i
$82$	−1.93156e7	+	1.62078e7i	−0.427222	+	0.358482i
$83$	−1.42612e7	−	2.47012e7i	−0.300500	−	0.520482i	0.675749	−	0.737132i	$-0.263820\pi$
$83$	−1.42612e7	−	2.47012e7i	−0.300500	−	0.520482i	−0.976249	+	0.216650i	$0.930487\pi$
$84$	4.96391e6	+	2.86591e6i	0.0997026	+	0.0575633i
$85$	−616386.	−	3.49570e6i	−0.0118080	−	0.0669666i
$86$	3.11323e6	−	548946.i	0.0569138	−	0.0100354i
$87$	−2.96485e7	+	5.13528e7i	−0.517519	+	0.896369i
$88$	5.04254e7	−	2.91131e7i	0.840850	−	0.485465i
$89$	−1.33770e6	−	1.59421e6i	−0.0213206	−	0.0254090i	0.755279	−	0.655404i	$-0.227501\pi$
$89$	−1.33770e6	−	1.59421e6i	−0.0213206	−	0.0254090i	−0.776599	+	0.629995i	$0.783057\pi$
$90$	−8.54815e6	−	2.34859e7i	−0.130287	−	0.357962i
$91$	2.41846e6	−	6.64466e6i	0.0352673	−	0.0968962i
$92$	2.85415e7	+	2.39492e7i	0.398406	+	0.334302i
$93$	−2.30520e7	+	1.30734e8i	−0.308161	+	1.74767i
$94$			4.43104e7i			0.567537i
$95$	−5.69913e7	−	1.92946e7i	−0.699704	−	0.236887i
$96$	1.12554e8			1.32519
$97$	−1.10420e8	−	1.94699e7i	−1.24727	−	0.219927i	−0.489239	−	0.872150i	$-0.662725\pi$
$97$	−1.10420e8	−	1.94699e7i	−1.24727	−	0.219927i	−0.758027	+	0.652223i	$0.773837\pi$
$98$	−3.68598e7	+	4.39278e7i	−0.399622	+	0.476251i
$99$	−7.02399e7	−	2.55652e7i	−0.731212	−	0.266139i
$100$	2.54916e7	−	9.27820e6i	0.254916	−	0.0927820i
$101$	−1.68150e7	+	1.41095e7i	−0.161589	+	0.135590i	−0.719997	−	0.693977i	$-0.755857\pi$
$101$	−1.68150e7	+	1.41095e7i	−0.161589	+	0.135590i	0.558408	+	0.829567i	$0.311412\pi$
$102$	4.25709e6	+	7.37350e6i	0.0393290	+	0.0681198i
$103$	−552924.	−	319231.i	−0.00491266	−	0.00283633i	0.497542	−	0.867440i	$-0.334236\pi$
$103$	−552924.	−	319231.i	−0.00491266	−	0.00283633i	−0.502454	+	0.864604i	$0.667569\pi$
$104$	−1.48277e7	−	8.40920e7i	−0.126748	−	0.718822i
$105$	1.70487e7	−	3.00615e6i	0.140260	−	0.0247316i
$106$	3.67514e7	−	6.36552e7i	0.291105	−	0.504209i
$107$	−1.56719e8	+	9.04815e7i	−1.19560	+	0.690279i	−0.959571	−	0.281467i	$-0.909179\pi$
$107$	−1.56719e8	+	9.04815e7i	−1.19560	+	0.690279i	−0.236028	+	0.971746i	$0.575846\pi$
$108$	1.31857e7	+	1.57141e7i	0.0969188	+	0.115503i
$109$	−1.22885e7	−	3.37623e7i	−0.0870546	−	0.239180i	0.888524	−	0.458829i	$-0.151731\pi$
$109$	−1.22885e7	−	3.37623e7i	−0.0870546	−	0.239180i	−0.975579	+	0.219649i	$0.929509\pi$
$110$	2.24878e7	−	6.17847e7i	0.153595	−	0.421998i
$111$	1.53450e8	+	1.28760e8i	1.01082	+	0.848179i
$112$	181177.	−	1.02750e6i	0.00115141	−	0.00652998i
$113$		−	2.57415e8i		−	1.57877i	−0.613896	−	0.789387i	$-0.710399\pi$
$113$		−	2.57415e8i		−	1.57877i	0.613896	−	0.789387i	$-0.289601\pi$
$114$	1.44285e8	−	3.26501e6i	0.854283	−	0.0193315i
$115$	1.12530e8			0.643397
$116$	−8.18612e7	−	1.44343e7i	−0.452112	−	0.0797196i
$117$	−7.04613e7	+	8.39725e7i	−0.376017	+	0.448119i
$118$	2.00718e8	+	7.30552e7i	1.03528	+	0.376811i
$119$	−2.48414e6	+	904154.i	−0.0123876	+	0.00450873i
$120$	1.60144e8	−	1.34377e8i	0.772299	−	0.648036i
$121$	8.85923e6	+	1.53446e7i	0.0413290	+	0.0715838i
$122$	−1.67858e8	−	9.69129e7i	−0.757710	−	0.437464i
$123$	4.70155e7	+	2.66638e8i	0.205410	+	1.16494i
$124$	−1.83267e8	+	3.23149e7i	−0.775170	+	0.136683i
$125$	1.31142e8	−	2.27144e8i	0.537157	−	0.930383i
$126$	−1.61198e7	+	9.30676e6i	−0.0639554	+	0.0369247i
$127$	−5.85866e7	−	6.98208e7i	−0.225208	−	0.268392i	0.641595	−	0.767044i	$-0.278273\pi$
$127$	−5.85866e7	−	6.98208e7i	−0.225208	−	0.268392i	−0.866803	+	0.498652i	$0.833829\pi$
$128$	5.12664e7	+	1.40853e8i	0.190982	+	0.524719i
$129$	1.16099e7	−	3.18978e7i	0.0419245	−	0.115187i
$130$	−7.38641e7	−	6.19794e7i	−0.258619	−	0.217007i
$131$	1.44108e7	−	8.17276e7i	0.0489331	−	0.277513i	−0.950517	−	0.310673i	$-0.899446\pi$
$131$	1.44108e7	−	8.17276e7i	0.0489331	−	0.277513i	0.999450	+	0.0331593i	$0.0105569\pi$
$132$		−	2.33757e8i		−	0.769960i
$133$	−6.78092e6	+	4.42945e7i	−0.0216712	+	0.141561i
$134$	−2.84799e8			−0.883322
$135$	6.10146e7	+	1.07585e7i	0.183696	+	0.0323905i
$136$	−2.05199e7	+	2.44546e7i	−0.0599817	+	0.0714835i
$137$	−6.74885e7	−	2.45638e7i	−0.191579	−	0.0697290i	0.244449	−	0.969662i	$-0.421393\pi$
$137$	−6.74885e7	−	2.45638e7i	−0.191579	−	0.0697290i	−0.436028	+	0.899933i	$0.643615\pi$
$138$	−2.53639e8	+	9.23172e7i	−0.699359	+	0.254546i
$139$	3.30258e8	−	2.77120e8i	0.884697	−	0.742349i	−0.0824422	−	0.996596i	$-0.526272\pi$
$139$	3.30258e8	−	2.77120e8i	0.884697	−	0.742349i	0.967139	+	0.254247i	$0.0818275\pi$
$140$	1.21340e7	+	2.10167e7i	0.0315858	+	0.0547082i
$141$	4.12052e8	+	2.37898e8i	1.04250	+	0.601887i
$142$	7.82066e7	+	4.43532e8i	0.192349	+	1.09087i
$143$	−2.83994e8	+	5.00758e7i	−0.679149	+	0.119752i
$144$	−8.08721e6	+	1.40075e7i	−0.0188083	+	0.0325769i
$145$	−2.17422e8	+	1.25529e8i	−0.491850	+	0.283969i
$146$	−2.14820e8	−	2.56013e8i	−0.472785	−	0.563443i
$147$	2.10598e8	+	5.78612e8i	0.451008	+	1.23913i
$148$	−9.60411e7	+	2.63871e8i	−0.200175	+	0.549977i
$149$	−2.08049e8	−	1.74574e8i	−0.422105	−	0.354188i	0.406858	−	0.913491i	$-0.366624\pi$
$149$	−2.08049e8	−	1.74574e8i	−0.422105	−	0.354188i	−0.828963	+	0.559303i	$0.811069\pi$
$150$	−3.41264e7	+	1.93540e8i	−0.0674101	+	0.382302i
$151$		−	4.88144e8i		−	0.938945i	−0.882947	−	0.469472i	$-0.844444\pi$
$151$		−	4.88144e8i		−	0.938945i	0.882947	−	0.469472i	$-0.155556\pi$
$152$	1.96531e8	+	5.04173e8i	0.368178	+	0.944507i
$153$	4.09814e7			0.0747862
$154$	−4.82230e7	−	8.50302e6i	−0.0857377	−	0.0151179i
$155$	−3.61282e8	+	4.30560e8i	−0.625922	+	0.745944i
$156$	−3.22132e8	−	1.17247e8i	−0.543921	−	0.197971i
$157$	6.63087e8	−	2.41344e8i	1.09137	−	0.397226i	0.267242	−	0.963629i	$-0.413888\pi$
$157$	6.63087e8	−	2.41344e8i	1.09137	−	0.397226i	0.824128	+	0.566403i	$0.191665\pi$
$158$	3.64483e8	−	3.05838e8i	0.584856	−	0.490752i
$159$	−3.94629e8	−	6.83518e8i	−0.617449	−	1.06945i
$160$	4.12699e8	+	2.38272e8i	0.629729	+	0.363574i
$161$	−1.45529e7	−	8.25334e7i	−0.0216593	−	0.122836i
$162$	−4.96122e8	+	8.74797e7i	−0.720325	+	0.127013i
$163$	−5.21577e8	+	9.03398e8i	−0.738870	+	1.27976i	0.214135	+	0.976804i	$0.431307\pi$
$163$	−5.21577e8	+	9.03398e8i	−0.738870	+	1.27976i	−0.953005	+	0.302956i	$0.902027\pi$
$164$	−3.28697e8	+	1.89773e8i	−0.454381	+	0.262337i
$165$	−4.53814e8	−	5.40835e8i	−0.612269	−	0.729674i
$166$	9.90696e7	+	2.72191e8i	0.130469	+	0.358461i
$167$	2.08250e8	−	5.72163e8i	0.267744	−	0.735621i	−0.730846	−	0.682542i	$-0.760874\pi$
$167$	2.08250e8	−	5.72163e8i	0.267744	−	0.735621i	0.998590	−	0.0530785i	$-0.0169034\pi$
$168$	−1.19267e8	−	1.00076e8i	−0.149721	−	0.125630i
$169$	6.82136e7	−	3.86859e8i	0.0836227	−	0.474248i
$170$			3.60482e7i			0.0431607i
$171$	3.33634e8	−	6.09303e8i	0.390199	−	0.712604i
$172$	4.75849e7			0.0543695
$173$	1.43448e9	+	2.52938e8i	1.60144	+	0.282377i	0.901812	−	0.432129i	$-0.142237\pi$
$173$	1.43448e9	+	2.52938e8i	1.60144	+	0.282377i	0.699629	+	0.714506i	$0.253349\pi$
$174$	3.87081e8	−	4.61305e8i	0.422284	−	0.503259i
$175$	−5.73394e7	−	2.08698e7i	−0.0611365	−	0.0222519i
$176$	−3.99842e7	+	1.45531e7i	−0.0416714	+	0.0151672i
$177$	1.75699e9	−	1.47429e9i	1.79010	−	1.50207i
$178$	1.05673e7	+	1.83031e7i	0.0105265	+	0.0182324i
$179$	7.80022e8	+	4.50346e8i	0.759792	+	0.438666i	0.829221	−	0.558921i	$-0.188784\pi$
$179$	7.80022e8	+	4.50346e8i	0.759792	+	0.438666i	−0.0694287	+	0.997587i	$0.522118\pi$
$180$	−6.53281e7	−	3.70494e8i	−0.0622315	−	0.352932i
$181$	1.00285e9	−	1.76830e8i	0.934378	−	0.164756i	0.314325	−	0.949316i	$-0.398222\pi$
$181$	1.00285e9	−	1.76830e8i	0.934378	−	0.164756i	0.620054	+	0.784559i	$0.287111\pi$
$182$	−3.59052e7	+	6.21897e7i	−0.0327244	+	0.0566804i
$183$	−1.80243e9	+	1.04063e9i	−1.60714	+	0.927882i
$184$	−6.50522e8	−	7.75262e8i	−0.567533	−	0.676359i
$185$	2.90071e8	+	7.96963e8i	0.247638	+	0.680380i
$186$	4.61096e8	−	1.26685e9i	0.385247	−	1.05846i
$187$	8.25877e7	+	6.92993e7i	0.0675381	+	0.0566712i
$188$	−1.15820e8	+	6.56850e8i	−0.0927158	+	0.525817i
$189$		−	4.61414e7i		−	0.0361612i
$190$	5.35957e8	+	2.93473e8i	0.411259	+	0.225192i
$191$	−1.71368e9			−1.28765			−0.643823	−	0.765175i	$-0.722653\pi$
$191$	−1.71368e9			−1.28765			−0.643823	+	0.765175i	$0.722653\pi$
$192$	−1.20910e9	−	2.13197e8i	−0.889730	−	0.156883i
$193$	−8.85882e8	+	1.05575e9i	−0.638479	+	0.760910i	−0.984129	−	0.177454i	$-0.943214\pi$
$193$	−8.85882e8	+	1.05575e9i	−0.638479	+	0.760910i	0.345650	+	0.938364i	$0.387658\pi$
$194$	1.06999e9	+	3.89446e8i	0.755396	+	0.274942i
$195$	−9.72929e8	+	3.54117e8i	−0.672888	+	0.244911i
$196$	−6.61225e8	+	5.54834e8i	−0.448048	+	0.375957i
$197$	−1.59745e8	−	2.76687e8i	−0.106063	−	0.183706i	0.808109	−	0.589033i	$-0.200491\pi$
$197$	−1.59745e8	−	2.76687e8i	−0.106063	−	0.183706i	−0.914172	+	0.405327i	$0.867158\pi$
$198$	6.57401e8	+	3.79550e8i	0.427730	+	0.246950i
$199$	−3.10979e8	−	1.76365e9i	−0.198298	−	1.12461i	−0.907643	−	0.419743i	$-0.862120\pi$
$199$	−3.10979e8	−	1.76365e9i	−0.198298	−	1.12461i	0.709345	−	0.704862i	$-0.248991\pi$
$200$	−7.25663e8	+	1.27954e8i	−0.453539	+	0.0799712i
$201$	−1.52906e9	+	2.64841e9i	−0.936785	+	1.62256i
$202$	1.93053e8	−	1.11459e8i	0.115950	−	0.0669437i
$203$	1.20185e8	+	1.43231e8i	0.0707726	+	0.0843435i
$204$	4.38333e7	+	1.20431e8i	0.0253095	+	0.0695373i
$205$	−3.92070e8	+	1.07720e9i	−0.221997	+	0.609933i
$206$	4.96695e6	+	4.16777e6i	0.00275817	+	0.00231438i
$207$	−2.25603e8	+	1.27946e9i	−0.122875	+	0.696859i
$208$			6.24004e7i			0.0333376i
$209$	1.70268e9	−	6.63722e8i	0.892377	−	0.347857i
$210$	−1.75809e8			−0.0903991
$211$	−2.32705e9	−	4.10322e8i	−1.17402	−	0.207012i	−0.447582	−	0.894243i	$-0.647715\pi$
$211$	−2.32705e9	−	4.10322e8i	−1.17402	−	0.207012i	−0.726439	+	0.687231i	$0.758826\pi$
$212$	7.11181e8	−	8.47553e8i	0.352076	−	0.419588i
$213$	4.54438e9	+	1.65402e9i	2.20778	+	0.803568i
$214$	1.72694e9	−	6.28554e8i	0.823421	−	0.299701i
$215$	1.10096e8	−	9.23812e7i	0.0515248	−	0.0432344i
$216$	−2.78597e8	−	4.82545e8i	−0.127986	−	0.221678i
$217$	3.62508e8	+	2.09294e8i	0.163485	+	0.0943883i
$218$	6.33603e7	+	3.59334e8i	0.0280538	+	0.159101i
$219$	−3.53407e9	+	6.23151e8i	−1.53638	+	0.270905i
$220$	4.94851e8	−	8.57107e8i	0.211244	−	0.365885i
$221$	1.36923e8	−	7.90526e7i	0.0573995	−	0.0331396i
$222$	−1.30762e9	−	1.55836e9i	−0.538355	−	0.641586i
$223$	−1.45168e9	−	3.98845e9i	−0.587017	−	1.61281i	−0.775929	−	0.630821i	$-0.782718\pi$
$223$	−1.45168e9	−	3.98845e9i	−0.587017	−	1.61281i	0.188912	−	0.981994i	$-0.439504\pi$
$224$	1.21384e8	−	3.33501e8i	0.0482138	−	0.132466i
$225$	7.24632e8	+	6.08038e8i	0.282740	+	0.237247i
$226$	−4.53947e8	+	2.57446e9i	−0.174009	+	0.986853i
$227$		−	2.97529e9i		−	1.12054i	−0.828311	−	0.560269i	$-0.810698\pi$
$227$		−	2.97529e9i		−	1.12054i	0.828311	−	0.560269i	$-0.189302\pi$
$228$	2.14739e9	+	3.28739e8i	0.794643	+	0.121650i
$229$	1.42217e9			0.517143			0.258572	−	0.965992i	$-0.416748\pi$
$229$	1.42217e9			0.517143			0.258572	+	0.965992i	$0.416748\pi$
$230$	−1.12544e9	−	1.98446e8i	−0.402172	−	0.0709137i
$231$	−3.37976e8	+	4.02785e8i	−0.118697	+	0.141457i
$232$	2.12170e9	+	7.72236e8i	0.732373	+	0.266562i
$233$	−8.82426e8	+	3.21177e8i	−0.299402	+	0.108973i	−0.487353	−	0.873205i	$-0.662038\pi$
$233$	−8.82426e8	+	3.21177e8i	−0.299402	+	0.108973i	0.187951	+	0.982178i	$0.439815\pi$
$234$	8.52782e8	−	7.15569e8i	0.284430	−	0.238665i
$235$	1.00724e9	+	1.74459e9i	0.330263	+	0.572033i
$236$	2.78445e9	+	1.60760e9i	0.897618	+	0.518240i
$237$	−8.87175e8	−	5.03142e9i	−0.281200	−	1.59477i
$238$	2.64389e7	−	4.66189e6i	0.00824016	−	0.00145296i
$239$	−1.26581e9	+	2.19244e9i	−0.387950	+	0.671949i	−0.992174	−	0.124866i	$-0.960150\pi$
$239$	−1.26581e9	+	2.19244e9i	−0.387950	+	0.671949i	0.604224	+	0.796815i	$0.293483\pi$
$240$	−1.32304e8	+	7.63855e7i	−0.0398774	+	0.0230232i
$241$	−3.63007e9	−	4.32615e9i	−1.07608	−	1.28243i	−0.957171	−	0.289524i	$-0.906503\pi$
$241$	−3.63007e9	−	4.32615e9i	−1.07608	−	1.28243i	−0.118914	−	0.992905i	$-0.537941\pi$
$242$	−6.15430e7	−	1.69088e8i	−0.0179439	−	0.0493005i
$243$	−1.54902e9	+	4.25589e9i	−0.444253	+	1.22058i
$244$	−2.23499e9	−	1.87538e9i	−0.630544	−	0.529089i
$245$	−4.52702e8	+	2.56740e9i	−0.125646	+	0.712573i
$246$		−	2.74962e9i		−	0.750813i
$247$	−6.06300e7	−	2.67932e9i	−0.0162892	−	0.719841i
$248$	5.05480e9			1.33628
$249$	3.06306e9	+	5.40101e8i	0.796817	+	0.140500i
$250$	−1.71214e9	+	2.04045e9i	−0.438308	+	0.522356i
$251$	5.72614e9	+	2.08414e9i	1.44267	+	0.525089i	0.940534	−	0.339700i	$-0.110326\pi$
$251$	5.72614e9	+	2.08414e9i	1.44267	+	0.525089i	0.502136	+	0.864789i	$0.332548\pi$
$252$	−2.63284e8	+	9.58274e7i	−0.0652862	+	0.0237622i
$253$	−2.61820e9	+	2.19693e9i	−0.639030	+	0.536209i
$254$	4.62809e8	+	8.01609e8i	0.111190	+	0.192587i
$255$	3.35220e8	+	1.93540e8i	0.0792811	+	0.0457730i
$256$	−7.64834e8	−	4.33759e9i	−0.178077	−	1.00992i
$257$	4.61523e9	−	8.13789e8i	1.05794	−	0.186543i	0.382497	−	0.923957i	$-0.375064\pi$
$257$	4.61523e9	−	8.13789e8i	1.05794	−	0.186543i	0.675441	+	0.737414i	$0.263953\pi$
$258$	−1.72364e8	+	2.98543e8i	−0.0389016	+	0.0673796i
$259$	5.47005e8	−	3.15813e8i	0.121560	−	0.0701829i
$260$	−9.32946e8	−	1.11184e9i	−0.204157	−	0.243304i
$261$	−9.91356e8	−	2.72373e9i	−0.213633	−	0.586951i
$262$	−2.88251e8	+	7.91962e8i	−0.0611738	+	0.168073i
$263$	8.16901e8	+	6.85461e8i	0.170744	+	0.143271i	0.724156	−	0.689637i	$-0.242230\pi$
$263$	8.16901e8	+	6.85461e8i	0.170744	+	0.143271i	−0.553411	+	0.832908i	$0.686674\pi$
$264$	−1.10257e9	+	6.25298e9i	−0.226981	+	1.28727i
$265$		−	3.34164e9i		−	0.677605i
$266$	1.45930e8	−	4.31041e8i	0.0291486	−	0.0860977i
$267$	2.26939e8			0.0446545
$268$	−4.22181e9	−	7.44420e8i	−0.818389	−	0.144304i
$269$	−1.85311e9	+	2.20845e9i	−0.353909	+	0.421773i	−0.913399	−	0.407064i	$-0.866552\pi$
$269$	−1.85311e9	+	2.20845e9i	−0.353909	+	0.421773i	0.559490	+	0.828837i	$0.310997\pi$
$270$	−5.91248e8	−	2.15196e8i	−0.111254	−	0.0404930i
$271$	−5.21882e9	+	1.89950e9i	−0.967598	+	0.352177i	−0.777007	−	0.629492i	$-0.783263\pi$
$271$	−5.21882e9	+	1.89950e9i	−0.967598	+	0.352177i	−0.190592	+	0.981669i	$0.561041\pi$
$272$	1.78709e7	−	1.49954e7i	0.00326490	−	0.00273958i
$273$	3.85544e8	+	6.67781e8i	0.0694102	+	0.120222i
$274$	6.31649e8	+	3.64683e8i	0.112066	+	0.0647013i
$275$	4.32124e8	+	2.45070e9i	0.0755575	+	0.428508i
$276$	−4.00121e9	+	7.05522e8i	−0.689533	+	0.121583i
$277$	−3.13270e9	+	5.42599e9i	−0.532108	+	0.921638i	0.467190	+	0.884157i	$0.345267\pi$
$277$	−3.13270e9	+	5.42599e9i	−0.532108	+	0.921638i	−0.999297	+	0.0374805i	$0.988067\pi$
$278$	−3.79168e9	+	2.18913e9i	−0.634823	+	0.366515i
$279$	−4.17110e9	−	4.97093e9i	−0.688390	−	0.820391i
$280$	−2.25453e8	−	6.19428e8i	−0.0366796	−	0.100776i
$281$	1.20808e9	−	3.31918e9i	0.193763	−	0.532359i	−0.804324	−	0.594192i	$-0.797472\pi$
$281$	1.20808e9	−	3.31918e9i	0.193763	−	0.532359i	0.998087	+	0.0618321i	$0.0196943\pi$
$282$	−3.70149e9	−	3.10592e9i	−0.585302	−	0.491127i
$283$	−1.88686e9	+	1.07009e10i	−0.294167	+	1.66830i	0.376403	+	0.926456i	$0.377161\pi$
$283$	−1.88686e9	+	1.07009e10i	−0.294167	+	1.66830i	−0.670570	+	0.741847i	$0.733950\pi$
$284$			6.77927e9i			1.04210i
$285$	5.60657e9	−	3.40835e9i	0.849802	−	0.516613i
$286$	2.92859e9			0.437718
$287$	8.40758e8	+	1.48248e8i	0.123921	+	0.0218505i
$288$	−3.53651e9	+	4.21465e9i	−0.514050	+	0.612621i
$289$	6.49952e9	+	2.36563e9i	0.931730	+	0.339122i
$290$	2.39586e9	−	8.72020e8i	0.338742	−	0.123292i
$291$	9.36625e9	−	7.85921e9i	1.30615	−	1.09599i
$292$	−2.51528e9	−	4.35660e9i	−0.345984	−	0.599261i
$293$	−1.02691e9	−	5.92886e8i	−0.139335	−	0.0804452i	0.428712	−	0.903441i	$-0.358968\pi$
$293$	−1.02691e9	−	5.92886e8i	−0.139335	−	0.0804452i	−0.568047	+	0.822996i	$0.692301\pi$
$294$	−1.08586e9	−	6.15821e9i	−0.145340	−	0.824261i
$295$	9.56329e9	−	1.68627e9i	1.26276	−	0.222658i
$296$	3.81370e9	−	6.60553e9i	0.496798	−	0.860480i
$297$	−1.62964e9	+	9.40873e8i	−0.209443	+	0.120922i
$298$	1.77288e9	+	2.11284e9i	0.224810	+	0.267918i
$299$	1.71429e9	+	4.70999e9i	0.214487	+	0.589298i
$300$	−1.01177e9	+	2.77981e9i	−0.124910	+	0.343186i
$301$	−8.19933e7	−	6.88005e7i	−0.00998877	−	0.00838158i
$302$	−8.60834e8	+	4.88203e9i	−0.103488	+	0.586912i
$303$		−	2.39365e9i		−	0.283982i
$304$	−7.74601e7	−	3.87780e8i	−0.00906951	−	0.0454036i
$305$	−8.81186e9			−1.01828
$306$	−4.09864e8	−	7.22701e7i	−0.0467470	−	0.00824276i
$307$	4.62205e7	−	5.50834e7i	0.00520332	−	0.00620108i	−0.763437	−	0.645883i	$-0.776489\pi$
$307$	4.62205e7	−	5.50834e7i	0.00520332	−	0.00620108i	0.768640	+	0.639682i	$0.220934\pi$
$308$	−6.92625e8	−	2.52095e8i	−0.0769654	−	0.0280131i
$309$	6.54241e7	−	2.38124e7i	0.00717635	−	0.00261198i
$310$	4.37255e9	−	3.66900e9i	0.473465	−	0.397284i
$311$	−7.85263e9	−	1.36012e10i	−0.839409	−	1.45390i	−0.890390	−	0.455199i	$-0.849568\pi$
$311$	−7.85263e9	−	1.36012e10i	−0.839409	−	1.45390i	0.0509808	−	0.998700i	$-0.483765\pi$
$312$	8.06400e9	+	4.65575e9i	0.851005	+	0.491328i
$313$	1.71629e9	+	9.73359e9i	0.178819	+	1.01413i	0.933642	+	0.358206i	$0.116612\pi$
$313$	1.71629e9	+	9.73359e9i	0.178819	+	1.01413i	−0.754823	+	0.655928i	$0.772277\pi$
$314$	−7.05728e9	+	1.24439e9i	−0.725971	+	0.128008i
$315$	−4.23112e8	+	7.32851e8i	−0.0429747	+	0.0744343i
$316$	6.20245e9	−	3.58099e9i	0.622035	−	0.359132i
$317$	−6.17152e9	−	7.35493e9i	−0.611160	−	0.728352i	0.368363	−	0.929682i	$-0.379918\pi$
$317$	−6.17152e9	−	7.35493e9i	−0.611160	−	0.728352i	−0.979524	+	0.201330i	$0.935474\pi$
$318$	2.74140e9	+	7.53193e9i	0.268080	+	0.736543i
$319$	2.60798e9	−	7.16537e9i	0.251850	−	0.691951i
$320$	−3.98204e9	−	3.34133e9i	−0.379757	−	0.318654i
$321$	3.42671e9	−	1.94338e10i	0.322743	−	1.83037i
$322$			8.51098e8i			0.0791691i
$323$	−7.52760e8	+	6.61230e8i	−0.0691587	+	0.0607495i
$324$	−7.58310e9			−0.688124
$325$	3.59397e9	+	6.33713e8i	0.322137	+	0.0568014i
$326$	6.80953e9	−	8.11528e9i	0.602902	−	0.718510i
$327$	3.68170e9	+	1.34003e9i	0.322001	+	0.117199i
$328$	9.68773e9	−	3.52604e9i	0.837002	−	0.304644i
$329$	1.14927e9	−	9.64356e8i	0.0980935	−	0.0823102i
$330$	3.58494e9	+	6.20930e9i	0.302292	+	0.523585i
$331$	4.57429e9	+	2.64097e9i	0.381076	+	0.220014i	0.678286	−	0.734798i	$-0.262723\pi$
$331$	4.57429e9	+	2.64097e9i	0.381076	+	0.220014i	−0.297210	+	0.954812i	$0.596056\pi$
$332$	7.57126e8	+	4.29388e9i	0.0623184	+	0.353425i
$333$	−9.64291e9	+	1.70031e9i	−0.784208	+	0.138277i
$334$	−3.09176e9	+	5.35508e9i	−0.248439	+	0.430308i
$335$	−1.12131e10	+	6.47388e9i	−0.890320	+	0.514026i
$336$	7.31336e7	+	8.71572e7i	0.00573799	+	0.00683827i
$337$	−1.22014e9	−	3.35232e9i	−0.0946001	−	0.259912i	0.883363	−	0.468690i	$-0.155274\pi$
$337$	−1.22014e9	−	3.35232e9i	−0.0946001	−	0.259912i	−0.977963	+	0.208778i	$0.933051\pi$
$338$	−1.36444e9	+	3.74876e9i	−0.104541	+	0.287224i
$339$	2.15033e10	+	1.80434e10i	1.62819	+	1.36622i
$340$	−9.42244e7	+	5.34373e8i	−0.00705095	+	0.0399879i
$341$		−	1.70710e10i		−	1.26253i
$342$	−4.41124e9	+	5.50541e9i	−0.322446	+	0.402425i
$343$	3.92377e9			0.283483
$344$	−1.27289e9	−	2.24445e8i	−0.0908988	−	0.0160279i
$345$	−7.88778e9	+	9.40029e9i	−0.556773	+	0.663536i
$346$	−1.39005e10	−	5.05937e9i	−0.969899	−	0.353014i
$347$	−1.04792e10	+	3.81413e9i	−0.722790	+	0.263074i	−0.677110	−	0.735882i	$-0.736768\pi$
$347$	−1.04792e10	+	3.81413e9i	−0.722790	+	0.263074i	−0.0456804	+	0.998956i	$0.514546\pi$
$348$	6.94381e9	−	5.82655e9i	0.473457	−	0.397278i
$349$	6.68352e9	+	1.15762e10i	0.450509	+	0.780305i	0.998418	−	0.0562336i	$-0.0179092\pi$
$349$	6.68352e9	+	1.15762e10i	0.450509	+	0.780305i	−0.547909	+	0.836538i	$0.684576\pi$
$350$	5.36660e8	+	3.09841e8i	0.0357624	+	0.0206474i
$351$	4.79199e8	+	2.71767e9i	0.0315709	+	0.179048i
$352$	−1.42539e10	+	2.51335e9i	−0.928460	+	0.163712i
$353$	−8.50164e9	+	1.47253e10i	−0.547525	+	0.948341i	0.450918	+	0.892565i	$0.351097\pi$
$353$	−8.50164e9	+	1.47253e10i	−0.547525	+	0.948341i	−0.998443	+	0.0557760i	$0.982237\pi$
$354$	−2.01719e10	+	1.16463e10i	−1.28450	+	0.741606i
$355$	1.31613e10	+	1.56850e10i	0.828674	+	0.987575i
$356$	1.08807e8	+	2.98944e8i	0.00677415	+	0.0186118i
$357$	9.85960e7	−	2.70890e8i	0.00606997	−	0.0166771i
$358$	−7.00699e9	−	5.87956e9i	−0.426579	−	0.357942i
$359$	5.27242e9	−	2.99014e10i	0.317419	−	1.80017i	−0.240907	−	0.970548i	$-0.577445\pi$
$359$	5.27242e9	−	2.99014e10i	0.317419	−	1.80017i	0.558325	−	0.829622i	$-0.311444\pi$
$360$			1.02188e10i			0.608403i
$361$	3.70272e9	+	1.65750e10i	0.218018	+	0.975945i
$362$	−1.03416e10			−0.602216
$363$	−1.90281e9	−	3.35516e8i	−0.109589	−	0.0193235i
$364$	−6.94808e8	+	8.28040e8i	−0.0395785	+	0.0471678i
$365$	−1.42774e10	−	5.19656e9i	−0.804411	−	0.292782i
$366$	1.98616e10	−	7.22903e9i	1.10685	−	0.402862i
$367$	−4.81494e9	+	4.04022e9i	−0.265416	+	0.222710i	−0.765777	−	0.643107i	$-0.777645\pi$
$367$	−4.81494e9	+	4.04022e9i	−0.265416	+	0.222710i	0.500361	+	0.865817i	$0.333201\pi$
$368$	3.69785e8	+	6.40486e8i	0.0201631	+	0.0349236i
$369$	−1.14616e10	−	6.61738e9i	−0.618217	−	0.356928i
$370$	−1.49563e9	−	8.48213e9i	−0.0798026	−	0.452583i
$371$	−2.45087e9	+	4.32154e8i	−0.129367	+	0.0228109i
$372$	1.01466e10	−	1.75744e10i	0.529843	−	0.917716i
$373$	3.99575e9	−	2.30695e9i	0.206425	−	0.119180i	−0.393224	−	0.919443i	$-0.628640\pi$
$373$	3.99575e9	−	2.30695e9i	0.206425	−	0.119180i	0.599649	+	0.800263i	$0.295307\pi$
$374$	−7.03769e8	−	8.38719e8i	−0.0359703	−	0.0428677i
$375$	9.78227e9	+	2.68766e10i	0.494669	+	1.35909i
$376$	6.19638e9	−	1.70244e10i	0.310018	−	0.851767i
$377$	−8.56626e9	−	7.18794e9i	−0.424059	−	0.355827i
$378$	−8.13695e7	+	4.61470e8i	−0.00398561	+	0.0226035i
$379$		−	3.61713e10i		−	1.75310i	−0.481308	−	0.876552i	$-0.659838\pi$
$379$		−	3.61713e10i		−	1.75310i	0.481308	−	0.876552i	$-0.340162\pi$
$380$	7.17785e9	+	5.75130e9i	0.344239	+	0.275824i
$381$	9.93912e9			0.471681
$382$	1.71389e10	+	3.02205e9i	0.804876	+	0.141921i
$383$	7.02420e9	−	8.37111e9i	0.326439	−	0.389034i	−0.577717	−	0.816237i	$-0.696056\pi$
$383$	7.02420e9	−	8.37111e9i	0.326439	−	0.389034i	0.904156	+	0.427203i	$0.140501\pi$
$384$	−1.53597e10	−	5.59049e9i	−0.706413	−	0.257113i
$385$	−2.09192e9	+	7.61397e8i	−0.0952143	+	0.0346552i
$386$	1.07217e10	−	8.99657e9i	0.482964	−	0.405255i
$387$	8.29642e8	+	1.43698e9i	0.0369868	+	0.0640630i
$388$	1.48435e10	+	8.56989e9i	0.654951	+	0.378136i
$389$	6.30726e9	+	3.57703e10i	0.275450	+	1.56215i	0.737529	+	0.675315i	$0.235992\pi$
$389$	6.30726e9	+	3.57703e10i	0.275450	+	1.56215i	−0.462080	+	0.886838i	$0.652897\pi$
$390$	1.03550e10	−	1.82586e9i	0.447600	−	0.0789239i
$391$	9.36932e8	−	1.62281e9i	0.0400867	−	0.0694323i
$392$	2.03047e10	−	1.17229e10i	0.859910	−	0.496469i
$393$	5.81704e9	+	6.93248e9i	0.243855	+	0.290615i
$394$	1.10971e9	+	3.04891e9i	0.0460495	+	0.126520i
$395$	7.39829e9	−	2.03266e10i	0.303909	−	0.834982i
$396$	8.75312e9	+	7.34474e9i	0.355944	+	0.298673i
$397$	1.88868e9	−	1.07112e10i	0.0760321	−	0.431199i	−0.922902	−	0.385035i	$-0.874189\pi$
$397$	1.88868e9	−	1.07112e10i	0.0760321	−	0.431199i	0.998934	−	0.0461639i	$-0.0146996\pi$
$398$			1.81870e10i			0.724819i
$399$	−3.22486e9	−	3.67125e9i	−0.127239	−	0.144851i
$400$	5.38478e8			0.0210343
$401$	−3.99951e10	−	7.05222e9i	−1.54678	−	0.272740i	−0.665888	−	0.746051i	$-0.731947\pi$
$401$	−3.99951e10	−	7.05222e9i	−1.54678	−	0.272740i	−0.880895	+	0.473312i	$0.843058\pi$
$402$	1.99629e10	−	2.37908e10i	0.764396	−	0.910972i
$403$	−2.35249e10	−	8.56238e9i	−0.891884	−	0.324619i
$404$	3.15312e9	−	1.14764e9i	0.118363	−	0.0430805i
$405$	−1.75448e10	+	1.47218e10i	−0.652120	+	0.547193i
$406$	−9.49408e8	−	1.64442e9i	−0.0349421	−	0.0605215i
$407$	−2.23081e10	−	1.28796e10i	−0.812988	−	0.469379i
$408$	−6.04497e8	−	3.42827e9i	−0.0218149	−	0.123719i
$409$	1.11822e9	−	1.97172e8i	0.0399608	−	0.00704616i	−0.153632	−	0.988128i	$-0.549097\pi$
$409$	1.11822e9	−	1.97172e8i	0.0399608	−	0.00704616i	0.193593	+	0.981082i	$0.437986\pi$
$410$	5.82080e9	−	1.00819e10i	0.205991	−	0.356786i
$411$	6.78253e9	−	3.91589e9i	0.237697	−	0.137235i
$412$	6.27354e7	+	7.47652e7i	0.00217733	+	0.00259484i
$413$	−2.47352e9	−	6.79594e9i	−0.0850189	−	0.233587i
$414$	4.51261e9	−	1.23983e10i	0.153612	−	0.422046i
$415$	1.00879e10	+	8.46472e9i	0.340100	+	0.285378i
$416$	−3.68585e9	+	2.09035e10i	−0.123073	+	0.697983i
$417$			4.70129e10i			1.55479i
$418$	−1.81994e10	+	3.63537e9i	−0.596144	+	0.119081i
$419$	−3.06844e9			−0.0995545			−0.0497773	−	0.998760i	$-0.515851\pi$
$419$	−3.06844e9			−0.0995545			−0.0497773	+	0.998760i	$0.515851\pi$
$420$	−2.60617e9	−	4.59537e8i	−0.0837539	−	0.0147681i
$421$	−1.06735e10	+	1.27202e10i	−0.339766	+	0.404917i	−0.908689	−	0.417474i	$-0.862916\pi$
$421$	−1.06735e10	+	1.27202e10i	−0.339766	+	0.404917i	0.568923	+	0.822391i	$0.307360\pi$
$422$	2.25497e10	+	8.20743e9i	0.711036	+	0.258796i
$423$	−2.18551e10	+	7.95459e9i	−0.682638	+	0.248460i
$424$	−2.30218e10	+	1.93175e10i	−0.712320	+	0.597707i
$425$	−6.82176e8	−	1.18156e9i	−0.0209094	−	0.0362161i
$426$	−4.25325e10	−	2.45562e10i	−1.29146	−	0.745627i
$427$	1.13958e9	+	6.46290e9i	0.0342795	+	0.194409i
$428$	2.72428e10	−	4.80364e9i	0.811852	−	0.143151i
$429$	1.57233e10	−	2.72336e10i	0.464211	−	0.804037i
$430$	−1.26400e9	+	7.29772e8i	−0.0369721	+	0.0213459i
$431$	2.86081e10	+	3.40938e10i	0.829048	+	0.988021i	0.999996	+	0.00274122i	$0.000872559\pi$
$431$	2.86081e10	+	3.40938e10i	0.829048	+	0.988021i	−0.170948	+	0.985280i	$0.554683\pi$
$432$	1.39265e8	+	3.82628e8i	0.00399860	+	0.0109861i
$433$	−1.16406e10	+	3.19823e10i	−0.331150	+	0.909827i	0.656664	+	0.754184i	$0.271967\pi$
$433$	−1.16406e10	+	3.19823e10i	−0.331150	+	0.909827i	−0.987813	+	0.155643i	$0.950255\pi$
$434$	−3.25644e9	−	2.73247e9i	−0.0917875	−	0.0770189i
$435$	4.75402e9	−	2.69614e10i	0.132771	−	0.752983i
$436$			5.49233e9i			0.151988i
$437$	−1.65000e10	−	2.71416e10i	−0.452436	−	0.744234i
$438$	3.64439e10			0.990212
$439$	4.09841e10	+	7.22660e9i	1.10346	+	0.194570i	0.695569	−	0.718459i	$-0.255152\pi$
$439$	4.09841e10	+	7.22660e9i	1.10346	+	0.194570i	0.407893	+	0.913030i	$0.366264\pi$
$440$	−1.72800e10	+	2.05935e10i	−0.461034	+	0.549439i
$441$	−2.82835e10	−	1.02943e10i	−0.747787	−	0.272172i
$442$	−1.50881e9	+	5.49160e8i	−0.0395316	+	0.0143883i
$443$	−1.66454e10	+	1.39672e10i	−0.432195	+	0.362655i	−0.832779	−	0.553605i	$-0.813252\pi$
$443$	−1.66454e10	+	1.39672e10i	−0.432195	+	0.362655i	0.400584	+	0.916260i	$0.368807\pi$
$444$	−1.53106e10	−	2.65188e10i	−0.393968	−	0.682372i
$445$	8.32110e8	+	4.80419e8i	0.0212198	+	0.0122512i
$446$	7.48496e9	+	4.24493e10i	0.189169	+	1.07283i
$447$	2.91662e10	−	5.14279e9i	0.730550	−	0.128816i
$448$	−1.93566e9	+	3.35267e9i	−0.0480527	+	0.0832298i
$449$	3.49555e10	−	2.01815e10i	0.860062	−	0.496557i	−0.00397114	−	0.999992i	$-0.501264\pi$
$449$	3.49555e10	−	2.01815e10i	0.860062	−	0.496557i	0.864033	+	0.503435i	$0.167931\pi$
$450$	−6.17493e9	−	7.35900e9i	−0.150585	−	0.179460i
$451$	−1.19081e10	−	3.27172e10i	−0.287830	−	0.790806i
$452$	−1.34585e10	+	3.69769e10i	−0.322435	+	0.885883i
$453$	4.07773e10	+	3.42162e10i	0.968336	+	0.812530i
$454$	−5.24688e9	+	2.97565e10i	−0.123503	+	0.700421i
$455$			3.26471e9i			0.0761726i
$456$	−5.58921e10	−	1.89224e10i	−1.29268	−	0.437641i
$457$	−1.10315e10			−0.252913			−0.126456	−	0.991972i	$-0.540360\pi$
$457$	−1.10315e10			−0.252913			−0.126456	+	0.991972i	$0.540360\pi$
$458$	−1.42235e10	−	2.50798e9i	−0.323254	−	0.0569983i
$459$	6.63159e8	−	7.90322e8i	0.0149406	−	0.0178055i
$460$	−1.61647e10	−	5.88345e9i	−0.361023	−	0.131402i
$461$	−2.98934e9	+	1.08803e9i	−0.0661869	+	0.0240900i	−0.374901	−	0.927065i	$-0.622323\pi$
$461$	−2.98934e9	+	1.08803e9i	−0.0661869	+	0.0240900i	0.308715	+	0.951155i	$0.400101\pi$
$462$	4.09048e9	−	3.43232e9i	0.0897855	−	0.0753390i
$463$	−2.07252e8	−	3.58970e8i	−0.00450997	−	0.00781150i	0.863762	−	0.503901i	$-0.168102\pi$
$463$	−2.07252e8	−	3.58970e8i	−0.00450997	−	0.00781150i	−0.868272	+	0.496089i	$0.834769\pi$
$464$	−1.42894e9	−	8.24998e8i	−0.0308277	−	0.0177984i
$465$	−1.06431e10	−	6.03598e10i	−0.227643	−	1.29103i
$466$	9.39172e9	−	1.65601e9i	0.199160	−	0.0351172i
$467$	2.43463e10	−	4.21689e10i	0.511876	−	0.886595i	−0.488029	−	0.872827i	$-0.662284\pi$
$467$	2.43463e10	−	4.21689e10i	0.511876	−	0.886595i	0.999905	−	0.0137677i	$-0.00438252\pi$
$468$	1.45119e10	−	8.37845e9i	0.302511	−	0.174655i
$469$	6.19826e9	+	7.38680e9i	0.128109	+	0.152674i
$470$	−6.99704e9	−	1.92242e10i	−0.143391	−	0.393965i
$471$	−2.63180e10	+	7.23082e10i	−0.534774	+	1.46928i
$472$	−6.69013e10	−	5.61368e10i	−1.34793	−	1.13105i
$473$	−7.57993e8	+	4.29879e9i	−0.0151433	+	0.0858820i
$474$			5.18848e10i			1.02784i
$475$	−2.31209e10	+	5.23201e8i	−0.454182	+	0.0102776i
$476$	4.04112e8			0.00787179
$477$	3.79941e10	+	6.69938e9i	0.733909	+	0.129408i
$478$	1.65259e10	−	1.96948e10i	0.316559	−	0.377260i
$479$	4.08881e10	+	1.48820e10i	0.776702	+	0.282696i	0.699797	−	0.714342i	$-0.253274\pi$
$479$	4.08881e10	+	1.48820e10i	0.776702	+	0.282696i	0.0769053	+	0.997038i	$0.475496\pi$
$480$	−4.88322e10	+	1.77735e10i	−0.919901	+	0.334817i
$481$	−2.89381e10	+	2.42819e10i	−0.540617	+	0.453632i
$482$	2.86760e10	+	4.96683e10i	0.531288	+	0.920218i
$483$	7.91454e9	+	4.56946e9i	0.145424	+	0.0839608i
$484$	−4.70334e8	−	2.66740e9i	−0.00857088	−	0.0486079i
$485$	5.09804e10	−	8.98923e9i	0.921375	−	0.162463i
$486$	2.29972e10	−	3.98323e10i	0.412221	−	0.713988i
$487$	7.36046e10	−	4.24956e10i	1.30855	−	0.755490i	0.326693	−	0.945131i	$-0.394066\pi$
$487$	7.36046e10	−	4.24956e10i	1.30855	−	0.755490i	0.981853	+	0.189641i	$0.0607324\pi$
$488$	5.09401e10	+	6.07081e10i	0.898216	+	1.07045i
$489$	−3.89060e10	−	1.06893e11i	−0.680427	−	1.86946i
$490$	9.05514e9	−	2.48788e10i	0.157076	−	0.431564i
$491$	2.56745e8	+	2.15434e8i	0.00441749	+	0.00370671i	0.644994	−	0.764188i	$-0.276860\pi$
$491$	2.56745e8	+	2.15434e8i	0.00441749	+	0.00370671i	−0.640576	+	0.767895i	$0.721304\pi$
$492$	7.18707e9	−	4.07599e10i	0.122657	−	0.695621i
$493$			4.18063e9i			0.0707707i
$494$	−4.11856e9	+	2.69033e10i	−0.0691572	+	0.451750i
$495$	3.45109e10			0.574824
$496$	−3.63781e9	−	6.41444e8i	−0.0601054	−	0.0105982i
$497$	9.80179e9	−	1.16813e10i	0.160650	−	0.191455i
$498$	−2.96819e10	−	1.08033e10i	−0.482585	−	0.175647i
$499$	1.02981e11	−	3.74822e10i	1.66095	−	0.604537i	0.670439	−	0.741965i	$-0.266106\pi$
$499$	1.02981e11	−	3.74822e10i	1.66095	−	0.604537i	0.990512	+	0.137428i	$0.0438835\pi$
$500$	−3.07140e10	+	2.57721e10i	−0.491423	+	0.412353i
$501$	3.31987e10	+	5.75018e10i	0.526951	+	0.912705i
$502$	−5.35930e10	−	3.09419e10i	−0.843904	−	0.487228i
$503$	−1.46795e10	−	8.32515e10i	−0.229318	−	1.30053i	−0.854255	−	0.519854i	$-0.825986\pi$
$503$	−1.46795e10	−	8.32515e10i	−0.229318	−	1.30053i	0.624937	−	0.780675i	$-0.285125\pi$
$504$	7.49482e9	−	1.32154e9i	0.116155	−	0.0204813i
$505$	5.06724e9	−	8.77672e9i	0.0779123	−	0.134948i
$506$	3.00594e10	−	1.73548e10i	0.458542	−	0.264739i
$507$	2.75350e10	+	3.28149e10i	0.416729	+	0.496638i
$508$	4.76533e9	+	1.30926e10i	0.0715547	+	0.196595i
$509$	9.43814e9	−	2.59311e10i	0.140610	−	0.386322i	−0.849321	−	0.527877i	$-0.822988\pi$
$509$	9.43814e9	−	2.59311e10i	0.140610	−	0.386322i	0.989930	+	0.141555i	$0.0452103\pi$
$510$	−3.01131e9	−	2.52679e9i	−0.0445117	−	0.0373497i
$511$	−1.96491e9	+	1.11435e10i	−0.0288177	+	0.163433i
$512$			6.35737e9i			0.0925119i
$513$	−6.35148e9	−	1.62938e10i	−0.0917076	−	0.235262i
$514$	−4.75930e10			−0.681852
$515$	2.90298e8	+	5.11874e7i	0.00412681	+	0.000727669i
$516$	−3.33544e9	+	3.97503e9i	−0.0470495	+	0.0560714i
$517$	−5.74945e10	−	2.09263e10i	−0.804756	−	0.292907i
$518$	−6.02764e9	+	2.19388e9i	−0.0837199	+	0.0304715i
$519$	−1.21679e11	+	1.02101e11i	−1.67705	+	1.40721i
$520$	1.97120e10	+	3.41422e10i	0.269598	+	0.466958i
$521$	−5.32935e10	−	3.07690e10i	−0.723308	−	0.417602i	0.0926611	−	0.995698i	$-0.470463\pi$
$521$	−5.32935e10	−	3.07690e10i	−0.723308	−	0.417602i	−0.815969	+	0.578096i	$0.803796\pi$
$522$	5.11151e9	+	2.89888e10i	0.0688442	+	0.390435i
$523$	−7.00273e10	+	1.23477e10i	−0.935968	+	0.165036i	−0.620773	−	0.783991i	$-0.713181\pi$
$523$	−7.00273e10	+	1.23477e10i	−0.935968	+	0.165036i	−0.315195	+	0.949027i	$0.602070\pi$
$524$	−6.34305e9	+	1.09865e10i	−0.0841343	+	0.145725i
$525$	5.76255e9	−	3.32701e9i	0.0758538	−	0.0437942i
$526$	−6.96120e9	−	8.29603e9i	−0.0909371	−	0.108375i
$527$	3.20110e9	+	8.79494e9i	0.0415008	+	0.114022i
$528$	1.58698e9	−	4.36019e9i	0.0204191	−	0.0561009i
$529$	−1.44826e10	−	1.21523e10i	−0.184937	−	0.155180i
$530$	−5.89293e9	+	3.34205e10i	−0.0746840	+	0.423554i
$531$			1.12114e11i			1.41020i
$532$	3.28992e9	−	6.00824e9i	0.0410713	−	0.0750068i
$533$	−5.10593e10			−0.632654
$534$	−2.26967e9	−	4.00204e8i	−0.0279124	−	0.00492171i
$535$	5.37050e10	−	6.40031e10i	0.655541	−	0.781243i
$536$	1.09422e11	+	3.98264e10i	1.32570	+	0.482516i
$537$	−9.22952e10	+	3.35927e10i	−1.10990	+	0.403969i
$538$	2.24279e10	−	1.88192e10i	0.267707	−	0.224633i
$539$	−3.95905e10	−	6.85728e10i	−0.469068	−	0.812450i
$540$	−8.20207e9	−	4.73547e9i	−0.0964603	−	0.0556914i
$541$	2.13667e10	+	1.21177e11i	0.249430	+	1.41459i	0.809976	+	0.586464i	$0.199480\pi$
$541$	2.13667e10	+	1.21177e11i	0.249430	+	1.41459i	−0.560546	+	0.828124i	$0.689409\pi$
$542$	5.55443e10	−	9.79395e9i	0.643639	−	0.113491i
$543$	−5.55229e10	+	9.61686e10i	−0.638665	+	1.10620i
$544$	6.87229e9	−	3.96772e9i	0.0784704	−	0.0453049i
$545$	1.06628e10	+	1.27074e10i	0.120861	+	0.144036i
$546$	−2.67828e9	−	7.35852e9i	−0.0301360	−	0.0827980i
$547$	−1.75216e10	+	4.81402e10i	−0.195715	+	0.537723i	−0.998266	−	0.0588602i	$-0.981253\pi$
$547$	−1.75216e10	+	4.81402e10i	−0.195715	+	0.537723i	0.802551	+	0.596584i	$0.203476\pi$
$548$	8.41024e9	+	7.05703e9i	0.0932581	+	0.0782528i
$549$	1.76662e10	−	1.00190e11i	0.194470	−	1.10290i
$550$		−	2.52720e10i		−	0.276178i
$551$	6.21566e10	+	3.40349e10i	0.674343	+	0.369248i
$552$	1.10360e11			1.18865
$553$	−1.58650e10	−	2.79742e9i	−0.169644	−	0.0299128i
$554$	4.08994e10	−	4.87420e10i	0.434188	−	0.517446i
$555$	−8.69071e10	−	3.16316e10i	−0.915974	−	0.333387i
$556$	−6.19293e10	+	2.25404e10i	−0.648033	+	0.235865i
$557$	−5.70734e10	+	4.78903e10i	−0.592943	+	0.497538i	−0.889169	−	0.457580i	$-0.848716\pi$
$557$	−5.70734e10	+	4.78903e10i	−0.592943	+	0.497538i	0.296226	+	0.955118i	$0.404272\pi$
$558$	3.29500e10	+	5.70710e10i	0.339874	+	0.588679i
$559$	5.54383e9	+	3.20073e9i	0.0567758	+	0.0327795i
$560$	8.36489e7	+	4.74396e8i	0.000850566	+	0.00482380i
$561$	−1.15779e10	+	2.04150e9i	−0.116890	+	0.0206109i
$562$	−1.79356e10	+	3.10653e10i	−0.179792	+	0.311409i
$563$	−2.44636e10	+	1.41241e10i	−0.243494	+	0.140581i	−0.616781	−	0.787134i	$-0.711564\pi$
$563$	−2.44636e10	+	1.41241e10i	−0.243494	+	0.140581i	0.373288	+	0.927716i	$0.378230\pi$
$564$	−4.67519e10	−	5.57167e10i	−0.462043	−	0.550642i
$565$	4.06483e10	+	1.11680e11i	0.398886	+	1.09593i
$566$	3.77418e10	−	1.03695e11i	0.367753	−	1.01039i
$567$	1.30664e10	+	1.09640e10i	0.126422	+	0.106081i
$568$	3.19760e10	−	1.81345e11i	0.307207	−	1.74226i
$569$			8.33466e10i			0.795131i	0.917574	+	0.397566i	$0.130145\pi$
$569$			8.33466e10i			0.795131i	−0.917574	+	0.397566i	$0.869855\pi$
$570$	−6.20830e10	+	2.42006e10i	−0.588130	+	0.229259i
$571$	−1.90282e10			−0.179000			−0.0894998	−	0.995987i	$-0.528527\pi$
$571$	−1.90282e10			−0.179000			−0.0894998	+	0.995987i	$0.528527\pi$
$572$	4.34130e10	+	7.65488e9i	0.405542	+	0.0715079i
$573$	1.20120e11	−	1.43153e11i	1.11428	−	1.32795i
$574$	−8.14717e9	−	2.96533e9i	−0.0750515	−	0.0273165i
$575$	4.06443e10	−	1.47933e10i	0.371816	−	0.135330i
$576$	4.59738e10	−	3.85766e10i	0.417658	−	0.350456i
$577$	−5.74791e10	−	9.95567e10i	−0.518569	−	0.898188i	−0.999767	−	0.0215760i	$-0.993132\pi$
$577$	−5.74791e10	−	9.95567e10i	−0.518569	−	0.898188i	0.481198	−	0.876612i	$-0.340202\pi$
$578$	−6.08314e10	−	3.51210e10i	−0.545025	−	0.314670i
$579$	−2.60973e10	−	1.48005e11i	−0.232210	−	1.31693i
$580$	3.77951e10	−	6.66430e9i	0.333983	−	0.0588901i
$581$	4.90369e9	−	8.49344e9i	0.0430347	−	0.0745383i
$582$	−1.07533e11	+	6.20844e10i	−0.937241	+	0.541117i
$583$	6.52388e10	+	7.77486e10i	0.564719	+	0.673005i
$584$	4.67348e10	+	1.28403e11i	0.401780	+	1.10388i
$585$	1.73098e10	−	4.75583e10i	0.147798	−	0.406072i
$586$	9.22478e9	+	7.74051e9i	0.0782286	+	0.0656416i
$587$	1.14238e10	−	6.47874e10i	0.0962181	−	0.545680i	−0.898149	−	0.439691i	$-0.855088\pi$
$587$	1.14238e10	−	6.47874e10i	0.0962181	−	0.545680i	0.994367	−	0.105989i	$-0.0338009\pi$
$588$		−	9.41266e10i		−	0.787414i
$589$	1.56822e11	+	2.40074e10i	1.30300	+	0.199473i
$590$	−9.86182e10			−0.813859
$591$	3.43104e10	+	6.04985e9i	0.281239	+	0.0495901i
$592$	−3.58285e9	+	4.26988e9i	−0.0291704	+	0.0347639i
$593$	−7.09669e10	−	2.58298e10i	−0.573901	−	0.208883i	0.0387329	−	0.999250i	$-0.487668\pi$
$593$	−7.09669e10	−	2.58298e10i	−0.573901	−	0.208883i	−0.612634	+	0.790367i	$0.709890\pi$
$594$	1.79576e10	−	6.53603e9i	0.144246	−	0.0525011i
$595$	9.34980e8	−	7.84541e8i	0.00745992	−	0.00625962i
$596$	2.07583e10	+	3.59545e10i	0.164516	+	0.284950i
$597$	1.69125e11	+	9.76445e10i	1.33141	+	0.768689i
$598$	−8.83904e9	−	5.01287e10i	−0.0691195	−	0.391996i
$599$	−1.14461e11	+	2.01826e10i	−0.889101	+	0.156773i	−0.599500	−	0.800375i	$-0.704634\pi$
$599$	−1.14461e11	+	2.01826e10i	−0.889101	+	0.156773i	−0.289601	+	0.957147i	$0.593523\pi$
$600$	4.01764e10	−	6.95875e10i	0.310003	−	0.536941i
$601$	−3.78286e10	+	2.18403e10i	−0.289949	+	0.167402i	−0.637919	−	0.770103i	$-0.720205\pi$
$601$	−3.78286e10	+	2.18403e10i	−0.289949	+	0.167402i	0.347970	+	0.937506i	$0.386871\pi$
$602$	6.98703e8	+	8.32682e8i	0.00531994	+	0.00634006i
$603$	−5.11270e10	−	1.40470e11i	−0.386706	−	1.06247i
$604$	−2.55217e10	+	7.01204e10i	−0.191762	+	0.526862i
$605$	−6.26668e9	−	5.25837e9i	−0.0467752	−	0.0392491i
$606$	−4.22117e9	+	2.39394e10i	−0.0312998	+	0.177510i
$607$			8.37751e10i			0.617107i	0.951207	+	0.308553i	$0.0998449\pi$
$607$			8.37751e10i			0.617107i	−0.951207	+	0.308553i	$0.900155\pi$
$608$	−3.04307e9	−	1.34477e11i	−0.0222689	−	0.984090i
$609$	−2.03891e10			−0.148228
$610$	8.81293e10	+	1.55396e10i	0.636504	+	0.112233i
$611$	−5.76757e10	+	6.87352e10i	−0.413836	+	0.493190i
$612$	−5.88686e9	−	2.14264e9i	−0.0419641	−	0.0152737i
$613$	2.12586e11	−	7.73749e10i	1.50554	−	0.547972i	0.548052	−	0.836444i	$-0.315370\pi$
$613$	2.12586e11	−	7.73749e10i	1.50554	−	0.547972i	0.957488	+	0.288472i	$0.0931474\pi$
$614$	−5.59399e8	+	4.69392e8i	−0.00393594	+	0.00330265i
$615$	−6.25027e10	−	1.08258e11i	−0.436916	−	0.756761i
$616$	1.73386e10	+	1.00105e10i	0.120418	+	0.0695234i
$617$	2.93920e10	+	1.66690e11i	0.202809	+	1.15019i	0.900850	+	0.434131i	$0.142944\pi$
$617$	2.93920e10	+	1.66690e11i	0.202809	+	1.15019i	−0.698040	+	0.716058i	$0.745944\pi$
$618$	−6.96313e8	+	1.22779e8i	−0.00477365	+	0.000841723i
$619$	−1.90526e10	+	3.30001e10i	−0.129775	+	0.224777i	−0.923589	−	0.383383i	$-0.874759\pi$
$619$	−1.90526e10	+	3.30001e10i	−0.129775	+	0.224777i	0.793814	+	0.608160i	$0.208092\pi$
$620$	7.44081e10	−	4.29596e10i	0.503563	−	0.290732i
$621$	2.10235e10	+	2.50548e10i	0.141364	+	0.168471i
$622$	5.45504e10	+	1.49876e11i	0.364449	+	1.00131i
$623$	2.44743e8	−	6.72426e8i	0.00162464	−	0.00446367i
$624$	−5.21265e9	−	4.37393e9i	−0.0343811	−	0.0288492i
$625$	−8.99067e9	+	5.09886e10i	−0.0589213	+	0.334159i
$626$		−	1.00374e11i		−	0.653620i
$627$	−6.39045e10	+	1.88758e11i	−0.413486	+	1.22133i
$628$	−1.07869e11			−0.693517
$629$	1.39082e10	+	2.45239e9i	0.0888524	+	0.0156671i
$630$	5.52400e9	−	6.58325e9i	0.0350664	−	0.0417905i
$631$	−1.25865e11	−	4.58109e10i	−0.793937	−	0.288969i	−0.0869652	−	0.996211i	$-0.527717\pi$
$631$	−1.25865e11	−	4.58109e10i	−0.793937	−	0.288969i	−0.706972	+	0.707242i	$0.749939\pi$
$632$	−1.82806e11	+	6.65359e10i	−1.14583	+	0.417049i
$633$	1.97390e11	−	1.65630e11i	1.22945	−	1.03163i
$634$	4.87524e10	+	8.44416e10i	0.301744	+	0.522636i
$635$	3.64434e10	+	2.10406e10i	0.224142	+	0.129409i
$636$	2.09508e10	+	1.18818e11i	0.128048	+	0.726194i
$637$	−1.14356e11	+	2.01640e10i	−0.694544	+	0.122467i
$638$	−3.87190e10	+	6.70632e10i	−0.233690	+	0.404764i
$639$	−2.04722e11	+	1.18196e11i	−1.22789	+	0.708926i
$640$	−4.44842e10	−	5.30142e10i	−0.265147	−	0.315989i
$641$	−9.85397e9	−	2.70736e10i	−0.0583686	−	0.160366i	0.907081	−	0.420956i	$-0.138305\pi$
$641$	−9.85397e9	−	2.70736e10i	−0.0583686	−	0.160366i	−0.965450	+	0.260590i	$0.916083\pi$
$642$	−6.85425e10	+	1.88319e11i	−0.403478	+	1.10855i
$643$	−2.23622e11	−	1.87641e11i	−1.30819	−	1.09770i	−0.988667	−	0.150124i	$-0.952033\pi$
$643$	−2.23622e11	−	1.87641e11i	−1.30819	−	1.09770i	−0.319523	−	0.947579i	$-0.603523\pi$
$644$	−2.22464e9	+	1.26165e10i	−0.0129335	+	0.0733494i
$645$			1.56723e10i			0.0905512i
$646$	8.69458e9	−	5.28563e9i	0.0499251	−	0.0303505i
$647$	−1.60398e11			−0.915341			−0.457671	−	0.889122i	$-0.651316\pi$
$647$	−1.60398e11			−0.915341			−0.457671	+	0.889122i	$0.651316\pi$
$648$	2.02847e11	+	3.57675e10i	1.15045	+	0.202856i
$649$	−1.89584e11	+	2.25938e11i	−1.06862	+	1.27353i
$650$	−3.48265e10	−	1.26758e10i	−0.195100	−	0.0710104i
$651$	−4.28934e10	+	1.56119e10i	−0.238817	+	0.0869225i
$652$	1.22155e11	−	1.02501e11i	0.675962	−	0.567200i
$653$	−1.05393e10	−	1.82546e10i	−0.0579640	−	0.100397i	0.835587	−	0.549358i	$-0.185128\pi$
$653$	−1.05393e10	−	1.82546e10i	−0.0579640	−	0.100397i	−0.893551	+	0.448961i	$0.851794\pi$
$654$	−3.44584e10	−	1.98945e10i	−0.188358	−	0.108748i
$655$	6.65342e9	+	3.77334e10i	0.0361476	+	0.205003i
$656$	−7.41946e9	+	1.30825e9i	−0.0400642	+	0.00706441i
$657$	8.77078e10	−	1.51914e11i	0.470735	−	0.815337i
$658$	−1.31948e10	+	7.61800e9i	−0.0703879	+	0.0406385i
$659$	−4.85405e10	−	5.78484e10i	−0.257373	−	0.306725i	0.621849	−	0.783137i	$-0.286382\pi$
$659$	−4.85405e10	−	5.78484e10i	−0.257373	−	0.306725i	−0.879222	+	0.476412i	$0.841937\pi$
$660$	3.69125e10	+	1.01416e11i	0.194535	+	0.534480i
$661$	8.12443e10	−	2.23217e11i	0.425586	−	1.16929i	−0.522879	−	0.852407i	$-0.675142\pi$
$661$	8.12443e10	−	2.23217e11i	0.425586	−	1.16929i	0.948465	−	0.316881i	$-0.102636\pi$
$662$	−4.10911e10	−	3.44795e10i	−0.213952	−	0.179527i
$663$	−2.99387e9	+	1.69791e10i	−0.0154946	+	0.0878740i
$664$		−	1.18432e11i		−	0.609252i
$665$	−4.05261e9	−	2.02881e10i	−0.0207228	−	0.103742i
$666$	9.94393e10			0.505430
$667$	−1.30521e11	−	2.30144e10i	−0.659443	−	0.116278i
$668$	−5.98290e10	+	7.13015e10i	−0.300473	+	0.358090i
$669$	4.34932e11	+	1.58302e11i	2.17128	+	0.790282i
$670$	1.23561e11	−	4.49725e10i	0.613172	−	0.223176i
$671$	2.05022e11	−	1.72034e11i	1.01137	−	0.848641i
$672$	1.93508e10	+	3.35165e10i	0.0948902	+	0.164355i
$673$	7.97336e10	+	4.60342e10i	0.388670	+	0.224399i	0.681584	−	0.731740i	$-0.261292\pi$
$673$	7.97336e10	+	4.60342e10i	0.388670	+	0.224399i	−0.292914	+	0.956139i	$0.594625\pi$
$674$	6.29116e9	+	3.56790e10i	0.0304854	+	0.172891i
$675$	2.34519e10	−	4.13520e9i	0.112970	−	0.0199196i
$676$	−3.00249e10	+	5.20046e10i	−0.143779	+	0.249032i
$677$	1.90751e11	−	1.10130e11i	0.908055	−	0.524266i	0.0282501	−	0.999601i	$-0.491007\pi$
$677$	1.90751e11	−	1.10130e11i	0.908055	−	0.524266i	0.879805	+	0.475335i	$0.157673\pi$
$678$	−1.83240e11	−	2.18376e11i	−0.867163	−	1.03344i
$679$	−1.31860e10	−	3.62281e10i	−0.0620344	−	0.170438i
$680$	5.04100e9	−	1.38500e10i	0.0235766	−	0.0647761i
$681$	2.48542e11	+	2.08552e11i	1.15561	+	0.969674i
$682$	−3.01044e10	+	1.70730e11i	−0.139153	+	0.789175i
$683$		−	2.40810e11i		−	1.10660i	−0.832982	−	0.553301i	$-0.813368\pi$
$683$		−	2.40810e11i		−	1.10660i	0.832982	−	0.553301i	$-0.186632\pi$
$684$	−7.97818e10	+	7.00810e10i	−0.364485	+	0.320166i
$685$	3.31590e10			0.150605
$686$	−3.92424e10	−	6.91950e9i	−0.177198	−	0.0312448i
$687$	−9.96867e10	+	1.18802e11i	−0.447518	+	0.533331i
$688$	8.87587e8	+	3.23055e8i	0.00396148	+	0.00144186i
$689$	1.39865e11	−	5.09067e10i	0.620629	−	0.225891i
$690$	9.54646e10	−	8.01043e10i	0.421159	−	0.353394i
$691$	−1.27744e10	−	2.21259e10i	−0.0560309	−	0.0970484i	0.836649	−	0.547739i	$-0.184511\pi$
$691$	−1.27744e10	−	2.21259e10i	−0.0560309	−	0.0970484i	−0.892680	+	0.450690i	$0.851178\pi$
$692$	−1.92835e11	−	1.11333e11i	−0.840932	−	0.485512i
$693$	−4.46307e9	−	2.53114e10i	−0.0193509	−	0.109744i
$694$	1.11531e11	−	1.96660e10i	0.480794	−	0.0847770i
$695$	−9.95239e10	+	1.72380e11i	−0.426568	+	0.738837i
$696$	−2.13229e11	+	1.23108e11i	−0.908676	+	0.524624i
$697$	1.22701e10	+	1.46229e10i	0.0519895	+	0.0619587i
$698$	−4.64289e10	−	1.27562e11i	−0.195599	−	0.537404i
$699$	3.50236e10	−	9.62266e10i	0.146707	−	0.403076i
$700$	7.14548e9	+	5.99577e9i	0.0297605	+	0.0249720i
$701$	−4.05775e10	+	2.30126e11i	−0.168040	+	0.953003i	0.777834	+	0.628470i	$0.216318\pi$
$701$	−4.05775e10	+	2.30126e11i	−0.168040	+	0.953003i	−0.945874	+	0.324533i	$0.894793\pi$
$702$		−	2.80251e10i		−	0.115398i
$703$	1.49690e11	−	1.86819e11i	0.612874	−	0.764892i
$704$	1.57881e11			0.642747
$705$	−2.16337e11	−	3.81460e10i	−0.875737	−	0.154416i
$706$	1.10995e11	−	1.32278e11i	0.446769	−	0.532438i
$707$	−7.09244e9	−	2.58144e9i	−0.0283869	−	0.0103320i
$708$	−3.29467e11	+	1.19916e11i	−1.31123	+	0.477248i
$709$	−1.11867e11	+	9.38679e10i	−0.442710	+	0.371477i	−0.836722	−	0.547628i	$-0.815531\pi$
$709$	−1.11867e11	+	9.38679e10i	−0.442710	+	0.371477i	0.394013	+	0.919105i	$0.371087\pi$
$710$	−1.03968e11	−	1.80078e11i	−0.409136	−	0.708644i
$711$	2.16279e11	+	1.24869e11i	0.846323	+	0.488625i
$712$	−1.50053e9	−	8.50994e9i	−0.00583882	−	0.0331136i
$713$	−2.92204e11	+	5.15234e10i	−1.13065	+	0.199364i
$714$	−1.46379e9	+	2.53536e9i	−0.00563230	+	0.00975544i
$715$	1.15304e11	−	6.65710e10i	0.441186	−	0.254719i
$716$	−8.85023e10	−	1.05473e11i	−0.336746	−	0.401318i
$717$	−9.44204e10	−	2.59418e11i	−0.357264	−	0.981575i
$718$	−1.05461e11	+	2.89752e11i	−0.396821	+	1.09026i
$719$	1.46944e11	+	1.23300e11i	0.549839	+	0.461369i	0.874886	−	0.484328i	$-0.160936\pi$
$719$	1.46944e11	+	1.23300e11i	0.549839	+	0.461369i	−0.325048	+	0.945698i	$0.605380\pi$
$720$	1.29675e9	−	7.35424e9i	0.00482532	−	0.0273658i
$721$		−	2.19533e8i		−	0.000812380i
$722$	−7.80191e9	−	1.72300e11i	−0.0287113	−	0.634069i
$723$	6.15835e11			2.25378
$724$	−1.53302e11	−	2.70313e10i	−0.557947	−	0.0983812i
$725$	−6.20276e10	+	7.39217e10i	−0.224509	+	0.267559i
$726$	1.84387e10	+	6.71113e9i	0.0663718	+	0.0241573i
$727$	1.82745e11	−	6.65139e10i	0.654197	−	0.238108i	0.00646809	−	0.999979i	$-0.497941\pi$
$727$	1.82745e11	−	6.65139e10i	0.654197	−	0.238108i	0.647729	+	0.761871i	$0.275719\pi$
$728$	2.24917e10	−	1.88728e10i	0.0800750	−	0.0671909i
$729$	−8.42066e10	−	1.45850e11i	−0.298151	−	0.516412i
$730$	1.33627e11	+	7.71498e10i	0.470548	+	0.271671i
$731$	−4.15579e8	−	2.35687e9i	−0.00145541	−	0.00825402i
$732$	3.13321e11	−	5.52469e10i	1.09130	−	0.192426i
$733$	2.13679e11	−	3.70102e11i	0.740194	−	1.28205i	−0.212213	−	0.977223i	$-0.568067\pi$
$733$	2.13679e11	−	3.70102e11i	0.740194	−	1.28205i	0.952407	−	0.304830i	$-0.0985995\pi$
$734$	5.52801e10	−	3.19160e10i	0.190452	−	0.109957i
$735$	−1.82737e11	−	2.17778e11i	−0.626148	−	0.746215i
$736$	8.60419e10	+	2.36398e11i	0.293224	+	0.805625i
$737$	1.34501e11	−	3.69538e11i	0.455885	−	1.25253i
$738$	1.02961e11	+	8.63942e10i	0.347093	+	0.291246i
$739$	−9.81429e10	+	5.56596e11i	−0.329064	+	1.86622i	0.150356	+	0.988632i	$0.451958\pi$
$739$	−9.81429e10	+	5.56596e11i	−0.329064	+	1.86622i	−0.479421	+	0.877585i	$0.659153\pi$
$740$		−	1.29647e11i		−	0.432351i
$741$	2.28068e11	+	1.82741e11i	0.756469	+	0.606126i
$742$	2.52737e10			0.0833784
$743$	−4.31829e11	−	7.61432e10i	−1.41696	−	0.249848i	−0.587865	−	0.808959i	$-0.700031\pi$
$743$	−4.31829e11	−	7.61432e10i	−1.41696	−	0.249848i	−0.829093	+	0.559111i	$0.811143\pi$
$744$	−3.54314e11	+	4.22255e11i	−1.15637	+	1.37811i
$745$	1.17830e11	+	4.28865e10i	0.382499	+	0.139218i
$746$	−4.40306e10	+	1.60258e10i	−0.142167	+	0.0517446i
$747$	−1.16467e11	+	9.77275e10i	−0.374043	+	0.313859i
$748$	−8.24028e9	−	1.42726e10i	−0.0263230	−	0.0455928i
$749$	−5.38873e10	−	3.11118e10i	−0.171222	−	0.0988549i
$750$	−5.04382e10	−	2.86049e11i	−0.159410	−	0.904057i
$751$	−1.07064e11	+	1.88783e10i	−0.336577	+	0.0593477i	−0.339383	−	0.940648i	$-0.610218\pi$
$751$	−1.07064e11	+	1.88783e10i	−0.336577	+	0.0593477i	0.00280535	+	0.999996i	$0.499107\pi$
$752$	−6.61974e9	+	1.14657e10i	−0.0207000	+	0.0358534i
$753$	−5.75471e11	+	3.32248e11i	−1.78996	+	1.03343i
$754$	7.29971e10	+	8.69946e10i	0.225850	+	0.269158i
$755$	7.70827e10	+	2.11783e11i	0.237230	+	0.651784i
$756$	−2.41242e9	+	6.62807e9i	−0.00738525	+	0.0202908i
$757$	2.58774e11	+	2.17137e11i	0.788019	+	0.661226i	0.945254	−	0.326335i	$-0.105814\pi$
$757$	2.58774e11	+	2.17137e11i	0.788019	+	0.661226i	−0.157236	+	0.987561i	$0.550258\pi$
$758$	−6.37875e10	+	3.61757e11i	−0.193223	+	1.09582i
$759$		−	3.72706e11i		−	1.12305i
$760$	−1.64880e11	−	1.87703e11i	−0.494212	−	0.562622i
$761$	−3.11494e11			−0.928777			−0.464388	−	0.885632i	$-0.653726\pi$
$761$	−3.11494e11			−0.928777			−0.464388	+	0.885632i	$0.653726\pi$
$762$	−9.94032e10	−	1.75275e10i	−0.294836	−	0.0519876i
$763$	7.94107e9	−	9.46380e9i	0.0234305	−	0.0279233i
$764$	2.46165e11	+	8.95967e10i	0.722525	+	0.262977i
$765$	−1.77799e10	+	6.47137e9i	−0.0519140	+	0.0188952i
$766$	−8.50128e10	+	7.13342e10i	−0.246927	+	0.207197i
$767$	2.16267e11	+	3.74585e11i	0.624896	+	1.08235i
$768$	4.15953e11	+	2.40151e11i	1.19564	+	0.690302i
$769$	−9.03546e10	−	5.12427e11i	−0.258372	−	1.46530i	−0.787267	−	0.616612i	$-0.788505\pi$
$769$	−9.03546e10	−	5.12427e11i	−0.258372	−	1.46530i	0.528895	−	0.848687i	$-0.322606\pi$
$770$	2.22645e10	−	3.92582e9i	0.0633358	−	0.0111678i
$771$	−2.55522e11	+	4.42577e11i	−0.723121	+	1.25248i
$772$	1.82452e11	−	1.05339e11i	0.513666	−	0.296565i
$773$	2.76974e10	+	3.30085e10i	0.0775748	+	0.0924501i	0.803436	−	0.595391i	$-0.203003\pi$
$773$	2.76974e10	+	3.30085e10i	0.0775748	+	0.0924501i	−0.725861	+	0.687841i	$0.758558\pi$
$774$	−5.76333e9	−	1.58346e10i	−0.0160587	−	0.0441208i
$775$	−7.38882e10	+	2.03006e11i	−0.204818	+	0.562733i
$776$	−3.56640e11	−	2.99257e11i	−0.983521	−	0.825272i
$777$	−1.19605e10	+	6.78311e10i	−0.0328143	+	0.186099i
$778$		−	3.68869e11i		−	1.00682i
$779$	3.17302e11	−	6.33819e10i	0.861634	−	0.172114i
$780$	1.58273e11			0.427590
$781$	−6.12435e11	−	1.07989e11i	−1.64610	−	0.290252i
$782$	−1.22323e10	+	1.45778e10i	−0.0327099	+	0.0389822i
$783$	−6.85688e10	−	2.49570e10i	−0.182423	−	0.0663966i
$784$	−1.61004e10	+	5.86007e9i	−0.0426160	+	0.0155110i
$785$	−2.49572e11	+	2.09416e11i	−0.657231	+	0.551482i
$786$	−4.59521e10	−	7.95914e10i	−0.120397	−	0.208534i
$787$	−1.47824e11	−	8.53465e10i	−0.385343	−	0.222478i	0.294797	−	0.955560i	$-0.404748\pi$
$787$	−1.47824e11	−	8.53465e10i	−0.385343	−	0.222478i	−0.680140	+	0.733082i	$0.738081\pi$
$788$	8.48083e9	+	4.80972e10i	0.0219955	+	0.124743i
$789$	−1.14521e11	+	2.01931e10i	−0.295512	+	0.0521068i
$790$	−1.09838e11	+	1.90244e11i	−0.281996	+	0.488431i
$791$	7.66531e10	−	4.42557e10i	0.195805	−	0.113048i
$792$	−1.99502e11	−	2.37758e11i	−0.507046	−	0.604274i
$793$	−1.34240e11	−	3.68822e11i	−0.339461	−	0.932662i
$794$	−3.77782e10	+	1.03795e11i	−0.0950516	+	0.261152i
$795$	2.79146e11	+	2.34231e11i	0.698815	+	0.586376i
$796$	−4.75381e10	+	2.69602e11i	−0.118410	+	0.671538i
$797$		−	7.92604e10i		−	0.196437i	−0.995165	−	0.0982184i	$-0.968686\pi$
$797$		−	7.92604e10i		−	0.196437i	0.995165	−	0.0982184i	$-0.0313144\pi$
$798$	2.57783e10	+	4.24039e10i	0.0635685	+	0.104567i
$799$	3.35451e10			0.0823080
$800$	1.80384e11	+	3.18066e10i	0.440391	+	0.0776529i
$801$	−7.13054e9	+	8.49784e9i	−0.0173218	+	0.0206433i
$802$	3.87563e11	+	1.41061e11i	0.936796	+	0.340966i
$803$	4.33639e11	−	1.57832e11i	1.04296	−	0.379605i
$804$	3.58112e11	−	3.00491e11i	0.857027	−	0.719131i
$805$	1.93466e10	+	3.35094e10i	0.0460704	+	0.0797963i
$806$	2.20178e11	+	1.27120e11i	0.521716	+	0.301213i
$807$	−5.45910e10	−	3.09601e11i	−0.128714	−	0.729975i
$808$	−8.97589e10	+	1.58269e10i	−0.210587	+	0.0371322i
$809$	−2.73296e11	+	4.73362e11i	−0.638026	+	1.10509i	0.347839	+	0.937554i	$0.386915\pi$
$809$	−2.73296e11	+	4.73362e11i	−0.638026	+	1.10509i	−0.985865	+	0.167539i	$0.946418\pi$
$810$	2.01431e11	−	1.16296e11i	0.467935	−	0.270162i
$811$	1.83573e11	+	2.18774e11i	0.424351	+	0.505722i	0.935284	−	0.353899i	$-0.115144\pi$
$811$	1.83573e11	+	2.18774e11i	0.424351	+	0.505722i	−0.510933	+	0.859621i	$0.670700\pi$
$812$	−9.77561e9	−	2.68583e10i	−0.0224864	−	0.0617809i
$813$	2.07136e11	−	5.69101e11i	0.474125	−	1.30265i
$814$	2.00395e11	+	1.68151e11i	0.456445	+	0.383003i
$815$	8.36327e10	−	4.74304e11i	0.189560	−	1.07505i
$816$			2.54395e9i			0.00573784i
$817$	−3.84247e10	−	1.30088e10i	−0.0862426	−	0.0291977i
$818$	−1.15313e10			−0.0257551
$819$	−3.71193e10	−	6.54514e9i	−0.0825020	−	0.0145473i
$820$	1.12639e11	−	1.34238e11i	0.249135	−	0.296907i
$821$	5.43747e11	+	1.97908e11i	1.19681	+	0.435602i	0.862109	−	0.506723i	$-0.169143\pi$
$821$	5.43747e11	+	1.97908e11i	1.19681	+	0.435602i	0.334698	+	0.942325i	$0.391366\pi$
$822$	−7.47391e10	+	2.72028e10i	−0.163705	+	0.0595836i
$823$	4.31100e11	−	3.61736e11i	0.939678	−	0.788483i	−0.0378514	−	0.999283i	$-0.512051\pi$
$823$	4.31100e11	−	3.61736e11i	0.939678	−	0.788483i	0.977529	+	0.210800i	$0.0676069\pi$
$824$	−1.32552e9	−	2.29587e9i	−0.00287527	−	0.00498011i
$825$	−2.35010e11	−	1.35683e11i	−0.507306	−	0.292893i
$826$	1.27537e10	+	7.23297e10i	0.0273978	+	0.155380i
$827$	4.05725e10	−	7.15403e9i	0.0867381	−	0.0152943i	−0.130111	−	0.991499i	$-0.541533\pi$
$827$	4.05725e10	−	7.15403e9i	0.0867381	−	0.0152943i	0.216849	+	0.976205i	$0.430422\pi$
$828$	9.93013e10	−	1.71995e11i	0.211268	−	0.365927i
$829$	1.19117e11	−	6.87720e10i	0.252205	−	0.145611i	−0.368568	−	0.929601i	$-0.620152\pi$
$829$	1.19117e11	−	6.87720e10i	0.252205	−	0.145611i	0.620774	+	0.783990i	$0.286819\pi$
$830$	−8.59634e10	−	1.02447e11i	−0.181135	−	0.215868i
$831$	−2.33678e11	−	6.42024e11i	−0.490019	−	1.34632i
$832$	7.91894e10	−	2.17571e11i	0.165262	−	0.454055i
$833$	3.32555e10	+	2.79047e10i	0.0690691	+	0.0579559i
$834$	8.29064e10	−	4.70186e11i	0.171366	−	0.971864i
$835$			2.81120e11i			0.578290i
$836$	−2.79287e11	+	6.31995e9i	−0.571775	+	0.0129386i
$837$	−1.63360e11			−0.332847
$838$	3.06881e10	+	5.41114e9i	0.0622291	+	0.0109727i
$839$	−1.37536e11	+	1.63909e11i	−0.277567	+	0.330791i	−0.886760	−	0.462231i	$-0.847049\pi$
$839$	−1.37536e11	+	1.63909e11i	−0.277567	+	0.330791i	0.609193	+	0.793022i	$0.291494\pi$
$840$	6.75473e10	+	2.45852e10i	0.135672	+	0.0493806i
$841$	−1.92223e11	+	6.99634e10i	−0.384256	+	0.139858i
$842$	1.29180e11	−	1.08395e11i	0.257008	−	0.215656i
$843$	1.92589e11	+	3.33574e11i	0.381348	+	0.660514i
$844$	3.12821e11	+	1.80607e11i	0.616489	+	0.355930i
$845$	3.14940e10	+	1.78612e11i	0.0617734	+	0.350334i
$846$	2.32605e11	−	4.10145e10i	0.454085	−	0.0800675i
$847$	−3.04622e9	+	5.27621e9i	−0.00591872	+	0.0102515i
$848$	1.90195e10	−	1.09809e10i	0.0367804	−	0.0212352i
$849$	−7.61647e11	−	9.07695e11i	−1.46596	−	1.74707i
$850$	4.73892e9	+	1.30201e10i	0.00907829	+	0.0249424i
$851$	−1.53130e11	+	4.20720e11i	−0.291972	+	0.802186i
$852$	−5.66309e11	−	4.75190e11i	−1.07472	−	0.901797i
$853$	−1.60795e11	+	9.11911e11i	−0.303721	+	1.72249i	0.325742	+	0.945459i	$0.394386\pi$
$853$	−1.60795e11	+	9.11911e11i	−0.303721	+	1.72249i	−0.629463	+	0.777031i	$0.716725\pi$
$854$		−	6.66465e10i		−	0.125298i
$855$	−4.85336e10	+	3.17032e11i	−0.0908193	+	0.593252i
$856$	−7.51401e11			−1.39951
$857$	7.58115e11	+	1.33676e11i	1.40544	+	0.247817i	0.824376	−	0.566043i	$-0.191526\pi$
$857$	7.58115e11	+	1.33676e11i	1.40544	+	0.247817i	0.581062	+	0.813859i	$0.302637\pi$
$858$	−2.05278e11	+	2.44641e11i	−0.378786	+	0.451420i
$859$	1.46461e11	+	5.33073e10i	0.268997	+	0.0979071i	0.472997	−	0.881064i	$-0.343172\pi$
$859$	1.46461e11	+	5.33073e10i	0.268997	+	0.0979071i	−0.204000	+	0.978971i	$0.565394\pi$
$860$	−2.06449e10	+	7.51412e9i	−0.0377415	+	0.0137368i
$861$	−7.13166e10	+	5.98417e10i	−0.129771	+	0.108891i
$862$	−2.25992e11	−	3.91429e11i	−0.409321	−	0.708964i
$863$	1.70275e11	+	9.83080e10i	0.306977	+	0.177233i	0.645573	−	0.763698i	$-0.276619\pi$
$863$	1.70275e11	+	9.83080e10i	0.306977	+	0.177233i	−0.338596	+	0.940932i	$0.609952\pi$
$864$	2.40514e10	+	1.36402e11i	0.0431604	+	0.244775i
$865$	−6.62297e11	+	1.16781e11i	−1.18301	+	0.208597i
$866$	1.72821e11	−	2.99334e11i	0.307273	−	0.532212i
$867$	−6.53196e11	+	3.77123e11i	−1.15602	+	0.667431i
$868$	−4.11306e10	−	4.90176e10i	−0.0724580	−	0.0863521i
$869$	2.24704e11	+	6.17368e11i	0.394032	+	1.08259i
$870$	−9.50919e10	+	2.61263e11i	−0.165984	+	0.456038i
$871$	−4.41786e11	−	3.70703e11i	−0.767608	−	0.644099i
$872$	2.59059e10	−	1.46919e11i	0.0448056	−	0.254105i
$873$			5.97663e11i			1.02896i
$874$	1.17156e11	+	3.00546e11i	0.200779	+	0.515069i
$875$	9.01855e10			0.153852
$876$	5.40238e11	+	9.52586e10i	0.917422	+	0.161766i
$877$	4.47279e11	−	5.33047e11i	0.756102	−	0.901087i	−0.241493	−	0.970403i	$-0.577637\pi$
$877$	4.47279e11	−	5.33047e11i	0.756102	−	0.901087i	0.997595	+	0.0693155i	$0.0220815\pi$
$878$	−3.97147e11	−	1.44550e11i	−0.668302	−	0.243242i
$879$	1.21508e11	−	4.42252e10i	0.203539	−	0.0740822i
$880$	1.50492e10	−	1.26278e10i	0.0250948	−	0.0210570i
$881$	6.92361e10	+	1.19920e11i	0.114929	+	0.199062i	0.917751	−	0.397156i	$-0.130003\pi$
$881$	6.92361e10	+	1.19920e11i	0.114929	+	0.199062i	−0.802823	+	0.596218i	$0.796669\pi$
$882$	2.64715e11	+	1.52833e11i	0.437425	+	0.252548i
$883$	−2.71870e10	−	1.54185e11i	−0.0447217	−	0.253629i	0.954248	−	0.299017i	$-0.0966588\pi$
$883$	−2.71870e10	−	1.54185e11i	−0.0447217	−	0.253629i	−0.998969	+	0.0453878i	$0.985548\pi$
$884$	−2.38017e10	+	4.19688e9i	−0.0389762	+	0.00687255i
$885$	−5.29472e11	+	9.17072e11i	−0.863117	+	1.49496i
$886$	1.91105e11	−	1.10335e11i	0.310126	−	0.179051i
$887$	6.98179e11	+	8.32058e11i	1.12790	+	1.34418i	0.931534	+	0.363655i	$0.118471\pi$
$887$	6.98179e11	+	8.32058e11i	1.12790	+	1.34418i	0.196371	+	0.980530i	$0.437084\pi$
$888$	2.84476e11	+	7.81591e11i	0.457503	+	1.25698i
$889$	1.07189e10	−	2.94498e10i	0.0171609	−	0.0471493i
$890$	−7.47490e9	−	6.27219e9i	−0.0119137	−	0.00999675i
$891$	1.20793e11	−	6.85053e11i	0.191660	−	1.08696i
$892$			6.48827e11i			1.02487i
$893$	2.73095e11	−	4.98741e11i	0.429445	−	0.784277i
$894$	−3.00767e11			−0.470847
$895$	−4.09530e11	−	7.22111e10i	−0.638254	−	0.112541i
$896$	−3.31294e10	+	3.94821e10i	−0.0514022	+	0.0612588i
$897$	−5.13614e11	−	1.86940e11i	−0.793353	−	0.288757i
$898$	−3.85187e11	+	1.40197e11i	−0.592333	+	0.215592i
$899$	5.07098e11	−	4.25506e11i	0.776342	−	0.651428i
$900$	−7.23009e10	−	1.25229e11i	−0.110198	−	0.190869i
$901$	−4.81901e10	−	2.78226e10i	−0.0731238	−	0.0422181i
$902$	6.13991e10	+	3.48212e11i	0.0927547	+	0.526038i
$903$	1.14946e10	−	2.02680e9i	0.0172879	−	0.00304832i
$904$	5.34424e11	−	9.25649e11i	0.800225	−	1.38603i
$905$	−4.07168e11	+	2.35079e11i	−0.606987	+	0.350444i
$906$	−3.47483e11	−	4.14114e11i	−0.515728	−	0.614621i
$907$	5.51055e10	+	1.51401e11i	0.0814264	+	0.223717i	0.973724	−	0.227730i	$-0.0731302\pi$
$907$	5.51055e10	+	1.51401e11i	0.0814264	+	0.223717i	−0.892298	+	0.451447i	$0.850908\pi$
$908$	−1.55558e11	+	4.27392e11i	−0.228849	+	0.628757i
$909$	8.96314e10	+	7.52096e10i	0.131282	+	0.110159i
$910$	5.75726e9	−	3.26510e10i	0.00839557	−	0.0476136i
$911$		−	5.66900e11i		−	0.823062i	−0.911396	−	0.411531i	$-0.864994\pi$
$911$		−	5.66900e11i		−	0.823062i	0.911396	−	0.411531i	$-0.135006\pi$
$912$	3.78229e10	+	2.07106e10i	0.0546733	+	0.0299373i
$913$	−3.99967e11			−0.575627
$914$	1.10329e11	+	1.94539e10i	0.158089	+	0.0278754i
$915$	6.17664e11	−	7.36103e11i	0.881187	−	1.05016i
$916$	−2.04291e11	−	7.43558e10i	−0.290180	−	0.105617i
$917$	2.68144e10	−	9.75966e9i	0.0379220	−	0.0138025i
$918$	−8.02611e9	+	6.73471e9i	−0.0113015	+	0.00948305i
$919$	−6.18295e11	−	1.07092e12i	−0.866829	−	1.50139i	−0.865220	−	0.501393i	$-0.832821\pi$
$919$	−6.18295e11	−	1.07092e12i	−0.866829	−	1.50139i	−0.00160931	−	0.999999i	$-0.500512\pi$
$920$	4.04653e11	+	2.33627e11i	0.564848	+	0.326115i
$921$	1.36161e9	+	7.72210e9i	0.00189241	+	0.0107324i
$922$	3.18158e10	−	5.60998e9i	0.0440269	−	0.00776314i
$923$	−4.55998e11	+	7.89812e11i	−0.628285	+	1.08822i
$924$	6.96082e10	−	4.01883e10i	0.0954932	−	0.0551330i
$925$	2.09539e11	+	2.49718e11i	0.286218	+	0.341101i
$926$	1.43973e9	+	3.95562e9i	0.00195811	+	0.00537986i
$927$	−1.16399e9	+	3.19803e9i	−0.00157627	+	0.00433076i
$928$	−4.29948e11	−	3.60769e11i	−0.579728	−	0.486449i
$929$	1.80569e11	−	1.02406e12i	0.242426	−	1.37487i	−0.583969	−	0.811776i	$-0.698501\pi$
$929$	1.80569e11	−	1.02406e12i	0.242426	−	1.37487i	0.826395	−	0.563091i	$-0.190388\pi$
$930$			6.22440e11i			0.832081i
$931$	6.85618e11	−	2.67260e11i	0.912606	−	0.355743i
$932$	1.43550e11			0.190256
$933$	1.68661e12	+	2.97394e11i	2.22580	+	0.392469i
$934$	−3.17856e11	+	3.78806e11i	−0.417680	+	0.497771i
$935$	−4.67740e10	−	1.70244e10i	−0.0612010	−	0.0222753i
$936$	−4.27711e11	+	1.55674e11i	−0.557247	+	0.202821i
$937$	−9.91698e11	+	8.32133e11i	−1.28653	+	1.07953i	−0.294225	+	0.955736i	$0.595062\pi$
$937$	−9.91698e11	+	8.32133e11i	−1.28653	+	1.07953i	−0.992308	+	0.123793i	$0.960494\pi$
$938$	−4.89636e10	−	8.48075e10i	−0.0632503	−	0.109553i
$939$	−9.33403e11	−	5.38901e11i	−1.20062	−	0.693180i
$940$	−5.34740e10	−	3.03266e11i	−0.0684906	−	0.388430i
$941$	6.62528e11	−	1.16822e11i	0.844978	−	0.148992i	0.265633	−	0.964074i	$-0.414419\pi$
$941$	6.62528e11	−	1.16822e11i	0.844978	−	0.148992i	0.579346	+	0.815082i	$0.303308\pi$
$942$	3.90727e11	−	6.76759e11i	0.496215	−	0.859469i
$943$	−5.24080e11	+	3.02578e11i	−0.662751	+	0.382640i
$944$	4.10235e10	+	4.88899e10i	0.0516588	+	0.0615646i
$945$	7.28617e9	+	2.00186e10i	0.00913634	+	0.0251019i
$946$	1.51617e10	−	4.16564e10i	0.0189314	−	0.0520137i
$947$	−3.39174e11	−	2.84601e11i	−0.421718	−	0.353864i	0.407098	−	0.913385i	$-0.366541\pi$
$947$	−3.39174e11	−	2.84601e11i	−0.421718	−	0.353864i	−0.828816	+	0.559521i	$0.810985\pi$
$948$	−1.35619e11	+	7.69132e11i	−0.167914	+	0.952287i
$949$		−	6.76749e11i		−	0.834377i
$950$	2.32160e11	+	3.55407e10i	0.285031	+	0.0436346i
$951$	1.04699e12			1.28003
$952$	−1.08100e10	−	1.90609e9i	−0.0131606	−	0.00232057i
$953$	1.51935e11	−	1.81069e11i	0.184198	−	0.219519i	−0.666041	−	0.745915i	$-0.732013\pi$
$953$	1.51935e11	−	1.81069e11i	0.184198	−	0.219519i	0.850240	+	0.526396i	$0.176457\pi$
$954$	−3.68172e11	−	1.34004e11i	−0.444486	−	0.161780i
$955$	7.43486e11	−	2.70607e11i	0.893840	−	0.325331i
$956$	2.96457e11	−	2.48757e11i	0.354920	−	0.297813i
$957$	4.15757e11	+	7.20112e11i	0.495669	+	0.858524i
$958$	−3.82686e11	−	2.20944e11i	−0.454340	−	0.262313i
$959$	−4.28825e9	−	2.43199e10i	−0.00506997	−	0.0287532i
$960$	5.58239e11	−	9.84327e10i	0.657257	−	0.115892i
$961$	3.14546e11	−	5.44810e11i	0.368800	−	0.638781i
$962$	3.32237e11	−	1.91817e11i	0.387925	−	0.223968i
$963$	6.20039e11	+	7.38934e11i	0.720965	+	0.859212i
$964$	2.95263e11	+	8.11229e11i	0.341902	+	0.939367i
$965$	2.17629e11	−	5.97932e11i	0.250962	−	0.689513i
$966$	−7.10969e10	−	5.96573e10i	−0.0816473	−	0.0685102i
$967$	1.82908e11	−	1.03733e12i	0.209184	−	1.18634i	−0.681535	−	0.731785i	$-0.738687\pi$
$967$	1.82908e11	−	1.03733e12i	0.209184	−	1.18634i	0.890719	−	0.454555i	$-0.150202\pi$
$968$			7.35712e10i			0.0837928i
$969$	−2.47177e9	−	1.09231e11i	−0.00280358	−	0.123894i
$970$	−5.25719e11			−0.593836
$971$	5.93560e11	+	1.04661e11i	0.667710	+	0.117735i	0.497221	−	0.867624i	$-0.334354\pi$
$971$	5.93560e11	+	1.04661e11i	0.667710	+	0.117735i	0.170490	+	0.985359i	$0.445465\pi$
$972$	4.45023e11	−	5.30357e11i	0.498560	−	0.594160i
$973$	1.39300e11	+	5.07011e10i	0.155418	+	0.0565673i
$974$	−8.11076e11	+	2.95207e11i	−0.901209	+	0.328013i
$975$	−3.04855e11	+	2.55804e11i	−0.337346	+	0.283067i
$976$	−2.89566e10	−	5.01542e10i	−0.0319115	−	0.0552724i
$977$	−9.65558e11	−	5.57465e11i	−1.05974	−	0.611842i	−0.134381	−	0.990930i	$-0.542905\pi$
$977$	−9.65558e11	−	5.57465e11i	−1.05974	−	0.611842i	−0.925361	+	0.379087i	$0.876238\pi$
$978$	2.00603e11	+	1.13767e12i	0.219271	+	1.24355i
$979$	−2.87396e10	+	5.06757e9i	−0.0312860	+	0.00551656i
$980$	1.99261e11	−	3.45131e11i	0.216032	−	0.374179i
$981$	−1.65859e11	+	9.57586e10i	−0.179086	+	0.103396i
$982$	−2.18784e9	−	2.60737e9i	−0.00235272	−	0.00280386i
$983$	4.18592e10	+	1.15007e11i	0.0448308	+	0.123172i	0.960088	−	0.279699i	$-0.0902347\pi$
$983$	4.18592e10	+	1.15007e11i	0.0448308	+	0.123172i	−0.915257	+	0.402871i	$0.868012\pi$
$984$	−3.84507e11	+	1.05643e12i	−0.410133	+	1.12683i
$985$	1.12998e11	+	9.48162e10i	0.120039	+	0.100725i
$986$	7.37247e9	−	4.18113e10i	0.00780019	−	0.0442371i
$987$			1.63601e11i			0.172392i
$988$	−1.31374e11	+	3.88046e11i	−0.137874	+	0.407244i
$989$	7.58702e10			0.0793024
$990$	−3.45150e11	−	6.08593e10i	−0.359309	−	0.0633558i
$991$	6.05547e11	−	7.21663e11i	0.627846	−	0.748238i	−0.354552	−	0.935036i	$-0.615367\pi$
$991$	6.05547e11	−	7.21663e11i	0.627846	−	0.748238i	0.982398	+	0.186798i	$0.0598111\pi$
$992$	−1.18074e12	−	4.29753e11i	−1.21929	−	0.443785i
$993$	−5.41247e11	+	1.96998e11i	−0.556671	+	0.202612i
$994$	−1.18630e11	+	9.95420e10i	−0.121520	+	0.101967i
$995$	4.13417e11	+	7.16059e11i	0.421790	+	0.730561i
$996$	−4.11761e11	−	2.37731e11i	−0.418416	−	0.241573i
$997$	2.49111e11	+	1.41278e12i	0.252123	+	1.42986i	0.803352	+	0.595505i	$0.203048\pi$
$997$	2.49111e11	+	1.41278e12i	0.252123	+	1.42986i	−0.551229	+	0.834354i	$0.685841\pi$
$998$	−1.09604e12	+	1.93261e11i	−1.10485	+	0.194815i
$999$	−1.23251e11	+	2.13477e11i	−0.123745	+	0.214333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.9.f.a.2.5	✓	72
19.10	odd	18	inner	19.9.f.a.10.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.9.f.a.2.5	✓	72	1.1	even	1	trivial
19.9.f.a.10.5	yes	72	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.0012 - 1.76348i) q^{2} +(-70.0946 + 83.5355i) q^{3} +(-143.647 - 52.2832i) q^{4} +(-433.854 + 157.910i) q^{5} +(848.344 - 711.845i) q^{6} +(171.924 + 297.780i) q^{7} +(3595.94 + 2076.12i) q^{8} +(-925.619 - 5249.44i) q^{9} +O(q^{10})\)	\(q+(-10.0012 - 1.76348i) q^{2} +(-70.0946 + 83.5355i) q^{3} +(-143.647 - 52.2832i) q^{4} +(-433.854 + 157.910i) q^{5} +(848.344 - 711.845i) q^{6} +(171.924 + 297.780i) q^{7} +(3595.94 + 2076.12i) q^{8} +(-925.619 - 5249.44i) q^{9} +(4617.53 - 814.196i) q^{10} +(7011.43 - 12144.1i) q^{11} +(14436.4 - 8334.85i) q^{12} +(-13218.7 - 15753.4i) q^{13} +(-1194.31 - 3281.35i) q^{14} +(17219.7 - 47310.8i) q^{15} +(-2324.45 - 1950.45i) q^{16} +(-1335.04 + 7571.41i) q^{17} +54133.1i q^{18} +(101701. + 81488.8i) q^{19} +70577.8 q^{20} +(-36926.1 - 6511.08i) q^{21} +(-91538.8 + 109092. i) q^{22} +(-229033. - 83361.3i) q^{23} +(-425486. + 154864. i) q^{24} +(-135943. + 114069. i) q^{25} +(104422. + 180864. i) q^{26} +(-116213. - 67095.7i) q^{27} +(-9127.39 - 51764.0i) q^{28} +(535510. - 94424.9i) q^{29} +(-255650. + 442799. i) q^{30} +(1.05427e6 - 608684. i) q^{31} +(-663458. - 790678. i) q^{32} +(523004. + 1.43694e6i) q^{33} +(26704.1 - 73368.9i) q^{34} +(-121612. - 102045. i) q^{35} +(-141496. + 802461. i) q^{36} -1.83694e6i q^{37} +(-873432. - 994335. i) q^{38} +2.24253e6 q^{39} +(-1.88795e6 - 332897. i) q^{40} +(1.59596e6 - 1.90199e6i) q^{41} +(357824. + 130237. i) q^{42} +(-292512. + 106466. i) q^{43} +(-1.64211e6 + 1.37789e6i) q^{44} +(1.23052e6 + 2.13133e6i) q^{45} +(2.14360e6 + 1.23761e6i) q^{46} +(-757660. - 4.29690e6i) q^{47} +(325863. - 57458.4i) q^{48} +(2.82329e6 - 4.89007e6i) q^{49} +(1.56075e6 - 901099. i) q^{50} +(-538902. - 642238. i) q^{51} +(1.07519e6 + 2.95405e6i) q^{52} +(-2.47545e6 + 6.80124e6i) q^{53} +(1.04395e6 + 875979. i) q^{54} +(-1.12425e6 + 6.37596e6i) q^{55} +1.42774e6i q^{56} +(-1.39359e7 + 2.78374e6i) q^{57} -5.52227e6 q^{58} +(-2.07133e7 - 3.65232e6i) q^{59} +(-4.94712e6 + 5.89575e6i) q^{60} +(1.79348e7 + 6.52773e6i) q^{61} +(-1.16174e7 + 4.22839e6i) q^{62} +(1.40405e6 - 1.17813e6i) q^{63} +(5.62943e6 + 9.75046e6i) q^{64} +(8.22260e6 + 4.74732e6i) q^{65} +(-2.69665e6 - 1.52935e7i) q^{66} +(2.76178e7 - 4.86976e6i) q^{67} +(587632. - 1.01781e6i) q^{68} +(2.30176e7 - 1.32892e7i) q^{69} +(1.03631e6 + 1.23503e6i) q^{70} +(-1.51678e7 - 4.16733e7i) q^{71} +(7.57000e6 - 2.07984e7i) q^{72} +(2.52093e7 + 2.11531e7i) q^{73} +(-3.23941e6 + 1.83716e7i) q^{74} -1.93517e7i q^{75} +(-1.03486e7 - 1.70229e7i) q^{76} +4.82172e6 q^{77} +(-2.24280e7 - 3.95466e6i) q^{78} +(-3.01155e7 + 3.58902e7i) q^{79} +(1.31647e6 + 479155. i) q^{80} +(4.66146e7 - 1.69663e7i) q^{81} +(-1.93156e7 + 1.62078e7i) q^{82} +(-1.42612e7 - 2.47012e7i) q^{83} +(4.96391e6 + 2.86591e6i) q^{84} +(-616386. - 3.49570e6i) q^{85} +(3.11323e6 - 548946. i) q^{86} +(-2.96485e7 + 5.13528e7i) q^{87} +(5.04254e7 - 2.91131e7i) q^{88} +(-1.33770e6 - 1.59421e6i) q^{89} +(-8.54815e6 - 2.34859e7i) q^{90} +(2.41846e6 - 6.64466e6i) q^{91} +(2.85415e7 + 2.39492e7i) q^{92} +(-2.30520e7 + 1.30734e8i) q^{93} +4.43104e7i q^{94} +(-5.69913e7 - 1.92946e7i) q^{95} +1.12554e8 q^{96} +(-1.10420e8 - 1.94699e7i) q^{97} +(-3.68598e7 + 4.39278e7i) q^{98} +(-7.02399e7 - 2.55652e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9}+O(q^{10}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9} - 2793 q^{10} + 10482 q^{11} - 124425 q^{12} + 108465 q^{13} + 91905 q^{14} - 236277 q^{15} - 207120 q^{16} + 40269 q^{17} + 188304 q^{19} + 1700646 q^{20} + 386850 q^{21} - 1237254 q^{22} - 1339566 q^{23} - 1289928 q^{24} + 59748 q^{25} - 842907 q^{26} + 4849875 q^{27} - 2065044 q^{28} - 1312269 q^{29} + 299940 q^{30} + 3498759 q^{31} + 9109881 q^{32} - 1670298 q^{33} - 12448236 q^{34} - 5923416 q^{35} - 6763797 q^{36} + 5067372 q^{38} + 18303516 q^{39} + 15014562 q^{40} - 11716206 q^{41} - 9228981 q^{42} + 12974721 q^{43} - 2631387 q^{44} - 31264995 q^{45} - 30318354 q^{46} + 1571889 q^{47} + 55683057 q^{48} + 1898838 q^{49} + 30782124 q^{50} + 12474372 q^{51} - 839439 q^{52} - 49160157 q^{53} - 65504571 q^{54} - 27903114 q^{55} + 18105312 q^{57} + 85061964 q^{58} + 51376881 q^{59} + 61200294 q^{60} - 51972462 q^{61} - 85396644 q^{62} + 41912118 q^{63} - 35891445 q^{64} + 2267586 q^{65} + 53209500 q^{66} + 35494521 q^{67} + 13755102 q^{68} + 54287784 q^{69} + 98126001 q^{70} - 5729388 q^{71} - 580668798 q^{72} - 255453906 q^{73} + 159588693 q^{74} + 128877954 q^{76} + 345629838 q^{77} + 120889431 q^{78} + 73477881 q^{79} - 93973551 q^{80} + 114909627 q^{81} + 67089591 q^{82} + 55994352 q^{83} + 143496459 q^{84} - 29709876 q^{85} - 592637892 q^{86} - 151341879 q^{87} - 412023537 q^{88} - 7283562 q^{89} + 350808846 q^{90} + 81065763 q^{91} + 496900692 q^{92} - 609570561 q^{93} - 222935505 q^{95} + 89754174 q^{96} - 180436449 q^{97} + 472058181 q^{98} + 865983036 q^{99}+O(q^{100}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9 - 2793 * q^10 + 10482 * q^11 - 124425 * q^12 + 108465 * q^13 + 91905 * q^14 - 236277 * q^15 - 207120 * q^16 + 40269 * q^17 + 188304 * q^19 + 1700646 * q^20 + 386850 * q^21 - 1237254 * q^22 - 1339566 * q^23 - 1289928 * q^24 + 59748 * q^25 - 842907 * q^26 + 4849875 * q^27 - 2065044 * q^28 - 1312269 * q^29 + 299940 * q^30 + 3498759 * q^31 + 9109881 * q^32 - 1670298 * q^33 - 12448236 * q^34 - 5923416 * q^35 - 6763797 * q^36 + 5067372 * q^38 + 18303516 * q^39 + 15014562 * q^40 - 11716206 * q^41 - 9228981 * q^42 + 12974721 * q^43 - 2631387 * q^44 - 31264995 * q^45 - 30318354 * q^46 + 1571889 * q^47 + 55683057 * q^48 + 1898838 * q^49 + 30782124 * q^50 + 12474372 * q^51 - 839439 * q^52 - 49160157 * q^53 - 65504571 * q^54 - 27903114 * q^55 + 18105312 * q^57 + 85061964 * q^58 + 51376881 * q^59 + 61200294 * q^60 - 51972462 * q^61 - 85396644 * q^62 + 41912118 * q^63 - 35891445 * q^64 + 2267586 * q^65 + 53209500 * q^66 + 35494521 * q^67 + 13755102 * q^68 + 54287784 * q^69 + 98126001 * q^70 - 5729388 * q^71 - 580668798 * q^72 - 255453906 * q^73 + 159588693 * q^74 + 128877954 * q^76 + 345629838 * q^77 + 120889431 * q^78 + 73477881 * q^79 - 93973551 * q^80 + 114909627 * q^81 + 67089591 * q^82 + 55994352 * q^83 + 143496459 * q^84 - 29709876 * q^85 - 592637892 * q^86 - 151341879 * q^87 - 412023537 * q^88 - 7283562 * q^89 + 350808846 * q^90 + 81065763 * q^91 + 496900692 * q^92 - 609570561 * q^93 - 222935505 * q^95 + 89754174 * q^96 - 180436449 * q^97 + 472058181 * q^98 + 865983036 * q^99

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